Motion- 1D and 2D JEE

 

Feb-2023

Question 1. An object moves with speed `u_1, u_2` and `u_3` along a line segment `AB, BC` and `CD` respectively as shown in figure. Where `AB = BC` and `AD = 3AB`, then average speed of the object will be:

प्रदर्शित चित्र में एक वस्तु रेखाखण्ड AB, BC  तथा CD पर क्रमशः `u_1, u_2` व `u_3` चाल से गति करता है। जहाँ `AB=BC` और `AD=3AB`, तव वस्तु की औसत चाल होगी:

(a) `{u_1u_2u_3}/{3(u_1u_2+u_2u_3+u_3u_1)}`

(b) `{(u_1+u_2+u_3)}/{3}`

(c) `{(u_1+u_2+u_3)}/{3u_1u_2u_3}`

(d) `{3u_1u_2u_3}/{(u_1u_2+u_2u_3+u_3u_1)}`

Answer (d)

Question 2. A child stands on the edge of the cliff  `10m` above the ground and throws a stone horizontally with an initial speed of  `5ms^-1`. Neglecting the air resistance, the speed with which the stone hits the ground will be `ms^-1` (given,`g=10ms^-2` )
एक बच्चा धरती के ऊपर `10` मी. की चट्टान के किनारे पर खडा और एक पत्थर को `5` मी./से. की प्रारम्भक चाल से क्षैतिज दिशा में फेकता है। वायु का प्रतिरोध नगण्य मानकर पत्थर धरती से जिस चाल से टकरात है वह __________ मी./से. होगी (दिया है,`g=10ms^-2` )

(a) `20`
(b) `25`
(c) `30`
(d) `15`

Answer (d)

Jan-2023

Question 3. The initial speed of a projectile fired from ground is `u`. At the highest point during its motion, the speed of projectile is `{\sqrt{3}}/{2}u`. The time of flight of the projectile is :

धरातल से दागे (छोडे) गए एक प्रक्षेप की प्रारम्भिक चाल `u` है। गति के दौरान अधिकतम ऊँचाई पर प्रक्षेप की चाल `{\sqrt{3}}/{2}u`. है । प्रक्षेप का उड्डयन काल है :

(a) `u/g`

(b) `{2u}/g`

(c) `u/{2g}`

(d) `{\sqrt{3}u}/g`

Answer (a)

 Question 4. Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following
{Assume negligible air friction}

(a) Metal ball will reach the earth's surface earlier than the insulating ball

(b) Both will reach the earth's surface simultaneously.

(c) Insulating ball will reach the earth's surface earlier than the metal ball

(d) Time taken by them to reach the earth's surface will be independent of the properties of their materials

समान आकार एवं समान द्रव्यमान वाले एक कुचालक गोले एवं एक धात्विक गोलाकार गेंद को समान ऊँचाई से गिराया जाता है। निम्न में से सही विकल्प चुनेंः (माना वायु का घर्षण नगण्य है)

 (a) धात्विक गेंद, पृथ्वी के तल पर, कुचालक गेंद से पहले पहुँचेगी।

(b) दोनों, पृथ्वी के तल पर एक साथ पहुँचेंगे।

(c) कुचालक गेंद, पूर्वी के तल पर धात्विक गेंद से पहले पहुँचेगी।

(d) पृथ्वी के तल तक पहुँचने में उनके द्वारा लिया गया समय, उनके पदार्थों के गुणों पर निर्भर नहीं करेगा।

 

 Answer (c) 

Question 5. A vehicle travels  `4Km` with speed of  `3Km/h` and another `4Km` with speed of  `5Km/h`, then its average speed is

एक वाहन प्रथम 4 किमी. को 3 किमी./घण्टा की चाल से तथा अन्य 4 किमी. को 5 किमी/घण्टा की चाल से चलता है तब इसकी औसत चाल है:

(a) `3.75`Km/h
(b) `4.25`Km/h
(c) `3.50`Km/h
(d) `4.00`Km/h

Answer (a)

Question 6. Match Column-I with Column-II :

	Column-I ($�$-t graphs)		Column-II ($�$-t graphs)
A.		I.
B.		II.
C.		III.
D.		IV.

Choose the correct answer from the options given below:

(a) A-II, B-III, C-IV, D-I

(b) A-II, B-IV, C-III, D-I

(c) A-I, B-III, C-IV, D-II

(d) A-I, B-II, C-III, D-IV

Answer (b)


Question 7. The distance travelled by a particle is related to time `t` as `x=4t^2`. The velocity of the particle at `t=5s` is :-

एक कण द्वारा तय की गई दूरी `x=4t^2` समय `t` से सम्बन्धित है।  `t=5s` पर कण वेग :

(a) `25 ms^-1`
(b) `20 ms^-1`
(c) `8 ms^-1`
(d) `40 ms^-1`

Answer (d)

Question 8. Two objects are projected with same velocity 'u' however at different angles `\alpha` and `\beta` with the horizontal. If  `\alpha+\beta = 90^o`, the ratio of horizontal range of the first object to the `2nd` object will be :

दो वस्तुओं को एक समान वेग 'u' से क्षैतिज के साथ क्रमशः `\alpha` व `\beta` कोण पर प्रक्षेपित किया जाता है। यदि  `\alpha+\beta = 90^o`, तो पहले वस्तु का दूसरी वस्तु के साथ क्षैतिज परास का अनुपात होगा :

(a) `1:1`
(b) `2:1`
(c) `1:2`
(d) `4:1`

Answer (a)

Question 9. A car travels a distance of `'x'` with speed `u_1` and then same distance `'x'` with speed `u_2` in the same direction. The average speed of the car is :

एक कार `u_1` चाल से `'x'` दूरी तय करती है, फिर उसी दिशा में `u_2` चाल से `'x'` दूरी तय करती है । कार की औसत चाल है:

(a) `{u_1u_2}/{2(u_1+u_2)}`

(b) `{2u_1u_2}/{(u_1+u_2)}`

(c)  `{2x}/{u_1+u_2}`

(d)  `{u_1+u_2}/2`

Answer (b)

Question 10. The velocity time graph of a body moving in a straight line is shown in the figure.
सरल रेखा में गतिमान एक पिण्ड का वेग - समय ग्राफ चित्र में प्रदर्शित किया गया हैय।

The ratio of displacement to distance travelled by the body in time `0` to `10s` is :

समय 0 से 10 s में पिण्ड द्वारा तय किये गये विस्थापन का दूरी के साथ अनुपात है :

(a) `1:1`
(b) `1:3`
(c) `1:4`
(d) `1:2`

Answer (b)

Question 11. The maximum vertical height to which a man can throw a ball is `136 m`. The maximum horizontal distance upto which he can throw the same ball is :

 एक व्यक्ति द्वारा गेंद को ऊर्ध्वाधर दिशा में  `136m` की अधिकतम ऊँचाई तक फेंका जा सकता है। उसके द्वारा उसी गेंद को फेंकी जा सकने वाली अधिकतम क्षैतिज दूरी है:

(a) `136m`
(b) `272m`
(c) `68m`
(d) `192m`

Answer (b)

JUL-2022

Question 12. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws `n` balls per second, the maximum height the balls can reach is

एक जगलर (गेंद उछालकर खेल दिखाने वाला) गेंदों को हवा में एक समान वेग से ऊध्र्वधरतः ऊपर की ओर फैंकता है । जब पहली गेंद अपनी अधिकतम ऊँचाई पर पहुँचती है, तब वह अगली गेंद फैंकता है । माना, जगलर `n` गेंदे प्रति सैकेंड फैंकता है । गेंदों द्वारा प्राप्त की जा सकने वाली अधिकतम ऊँचाई है:

(a) `g/{2n}`

(b) `g/n`

(c) `2gn`

(d) `g/{2n^2}`

Answer (d)


Question 13. A ball is released from a height `h`. If `t_1` and `t_2` be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between `t_1` and `t_2`.

एक गेंद h ऊँचाई से छोडी जाती है । यदि पहली आधी और अंतिम आधी दूरी को तय करने में क्रमशः `t_1` एवं `t_2` समय लगता है । तो `t_1` व `t_2` के बीच सही सम्बंध चुनें

(a) `t_1=(\sqrt{2})t_2`

(b) `t_1=(\sqrt{2}-1)t_2`

(c) `t_2=(\sqrt{2}+1)t_1`

(d) `t_2=(\sqrt{2}-1)t_1`

Answer (d)


Question 14. A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height `h`. Find the ratio of the times in which it is at height `h/3` while going up and coming down respectively.

एक गेंद को किसी निश्चित वेग से ऊपर की तरफ इस तरह फेंका जाता है कि यह `h` ऊँचाई तय करती है। उन समयों का अनुपात ज्ञात करो जब गेंद ऊपर जाते समय एवं नीचे आते समय `h/3` ऊँचाई पर है।

(a) `{\sqrt{2}-1}/{\sqrt{2}+1}`

(b) `{\sqrt{3}-\sqrt{2}}/{\sqrt{3}+\sqrt{2}}`

(c) `{\sqrt{3}-1}/{\sqrt{3}+1}`

(d) `1/3`

Answer (b)


Question 15. If  `t=\sqrt{x}+4`, then `({dx}/{dt})_{t=4}` is:

(a) `4`
(b) zero
(c) `8`
(d) `16`

Answer (b)


Question 16. At time `t=0` a particle starts travelling from a height `7\hat{z}cm` in a plane keeping `z` coordinate constant. At any instant of time it's position along the `\hat{x}` and `\hat{y}` directions are defined as `3t` and `5t^3` respectively. At `t = 1s` acceleration of the particle will be

समय `t=0`  पर, कोई कण `7\hat{z}cm` की ऊँचाई से एक तल में स्थिर `z` के साथ चलना प्रारम्भ करता है। किसी क्षण पर, `\hat{x}` एवं `\hat{y}`  दिशाओं के अनुदिश इसकी स्थिति क्रमशः `3t` एवं `5t^3` द्वारा परिभाषित है। समय  `t = 1s` पर, कण के त्वरण का मान होगा

 

(a) `-30\hat{y}`

(b) `30\hat{y}`

(c) `3\hat{x}+15\hat{y}`

(d) `3\hat{x}+15\hat{y}+7\hat{z}`

Answer (b)

Question 17. A NCC parade is going at a uniform speed of  `9km/h` under a mango tree on which a monkey is sitting at a height of  `19.6m`. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given `g=9.8m/s^2`)

एक NCC की परेड  `9km/h` की एकसमान चाल से किसी आम के पेड के नीचे से गुजर रही है, जिस पर एक बंदर  `19.6m` की ऊँचाई पर बैठा है। किसी क्षण विशेष पर, बंदर एक आम गिराता है। वह कैडेट (छात्र) उस आम को प्राप्त करेगा जिसकी दूरी गिराने के समय पर पेड से निम्न के बराबर है।

( दिया है, `g=9.8m/s^2`)

(a) `5m`
(b) `10m`
(c) `19.8m`
(d) `24.5m`

Answer (a)


Question 18. The velocity of the bullet becomes one third after it penetrates `4 cm` in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at `(4 + x) cm` inside the block. The value of `x` is :

किसी गोली का वेग एक तिहाई हो जाता है जब यह एक लकडी के गुटके को  `4cm` तक भेदती है। माना गुटके में गति के दौरान, गोली एक नियत प्रतिरोध का अनुभव कर रही है। गोली गुटके के अन्दर `(4+x)` पर रुक जाती है। `x` का मान है :

(a) `2.0`
(b) `1.0`
(c) `0.5`
(d) `1.5`

Answer (c)


Question 19. A bullet is shot vertically downwards with an initial velocity of  `100m/s` from a certain height. Within `10 s`, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time  `t=20s` will be:

(Take `g = 10 m/s^2`).

किसी नियत ऊँचाईं से, एक गोली  `100m/s` के प्रारमिक वेग से उध्वाधरतः नीचे की ओर दागी जाती है । यह गोली  `10s` में धरातल पर पहुँचती है, एवं उसी क्षण आदर्श अप्रत्यास्थ संघट्ट के कारण विश्राम अवस्था में आ जाती है । कुल समय  `t=20s` के लिए, वेग-समय वक्र आरेख होगा :

(यदि `g = 10 m/s^2`).

(a)


(b)


(c)


(d)



Answer (a)

Question 20. Two projectiles are thrown with same initial velocity making an angle of `45^o` and `30^o` with the horizontal respectively. The ratio of their respective ranges will be :

दो प्रक्षेप्य समान प्रारम्भिक वेग से, क्षैतिज से क्रमशः `45^o` और `30^o` के कोण पर प्रक्षेपित किए गए। उनके द्वारा तय किये गये परासों का अनुपात होगा:

(a) `1:\sqrt{2}`
(b) `\sqrt{2}:1`
(c) `2:\sqrt{3}`
(d) `\sqrt{3}:2`

Answer (c)


Question 21. A ball is projected from the ground with a speed `15 ms^-1` at an angle `\theta` with horizontal so that its range and maximum height are equal, then `'tan\theta'` will be equal to :

एक गेंद क्षैतिज तल से `\theta` कोण पर  `15 ms^-1` की चाल से इस प्रकार प्रक्षेपित की जाती है कि इसके द्वारा तय की गई दूरी एवं अधिकतम ऊँचाई का मान समान है, तो `'tan\theta'` का मान होगा:

(a) `1/4`

(b) `1/2`

(c) `2`

(d) `4`

Answer (d)


Question 22. At `t = 0`, truck, starting from rest, moves in the positive x-direction at uniform acceleration of `5 ms^-2`. At `t = 20 s`, a ball is released from the top of the truck. The ball strikes the ground in `1 s` after the release. The velocity of the ball, when it strikes the ground, will be :

(Given `g=10ms^-2` )

(a) `100\hat{i}-10\hat{j}`
(b) `10\hat{i}-100\hat{j}`
(c) `100\hat{i}`
(d) `-10\hat{j}`

Answer (a)

Jun-2022

Question 23. Two projectiles `P_1` and `P_2` thrown with speed in the ratio `\sqrt{3}: \sqrt{2}`, attain the same height during their motion. If `P_2` is thrown at an angle of `60^o` with the horizontal, the angle of projection of `P_1` with horizontal will be :

(a) `15^o`
(b) `30^o`
(c) `45^o`
(d) `60^o`

Answer (c)


Question 24. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of `10m` in `t s`, the distance travelled by the toy in the next `t s` will be:

एक छोटा खिलौना, विश्रामावस्था से एक स्थिर त्वरण के अन्तर्गत चलना प्रारम्भ करता है । यदि यह `ts` समय में `10 m` की दूरी तय करता है । तो अगले `ts` समय में खिलौने द्वारा तय की गई दूरी का मान होगा :

(a) `10m`
(b) `20m`
(c) `30m`
(d) `40m`

Answer (c)


Question 25. A person can throw a ball upto a maximum range of `100 m`. How high above the ground he can throw the same ball?
एक व्यक्ति किसी गेंद को `100 m` की अधिकतम दूरी तक फेंक सकता है । वह उसी गेंद को धरातल से कितनी अधिकतम ऊँचाई तक फेंक सकता है ?

(a) `25m`
(b) `50m`
(c) `100m`
(d) `200m`

Answer (b)


Question 26. Two balls A and B are placed at the top of `180 m` tall tower. Ball A is released from the top at `t = 0 s`. Ball B is thrown vertically down with an initial velocity `'u'` at `t = 2 s`. After a certain time, both balls meet `100 m` above the ground. Find the value of `'u'` in `ms^-1`. `[use  g = 10 ms^-2]` :

(a) `10`
(b) `15`
(c) `20`
(d) `30`

Answer (d)


Question 27. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as `u_2=n/m^2 u_1`  and `a_2=a_1/{mn}`  respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

(a) `n^3/m^3L_1=L_2 & n^2/m T_1=T_2`

(b) `L_1=n^4/m^2L_2 & T_1=n^2/mT_2`

(c) `L_1=n^2/mL_2 & T_1=n^4/m^2T_2`

(d) `n^2/mL_1=L_2 & n^4/m^4T_1=T_2`

Answer (a)

Question 28. A projectile is launched at an angle `'\alpha'` with the horizontal with a velocity `20 ms^-1`. After `10 s`, its inclination with horizontal is `'\beta'`. The value of `tan\beta` will be : (`g = 10 ms^-2`).

(a) `tan\alpha+5sec\alpha`
(b) `tan\alpha-5sec\alpha`
(c) `2tan\alpha-5sec\alpha`
(d) `2tan\alpha+5sec\alpha`

Answer (b)


Question 29. A girl standing on road holds her umbrella at `45^o` with the vertical to keep the rain away. If she starts running without umbrella with a speed of `15\sqrt{2} kmh^-1`, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

(a) `30kmh^-1`

(b) `{25}/\sqrt{2}kmh^-1`

(c) `{30}/\sqrt{2}kmh^-1`

(d) `25kmh^-1`

Answer (c)


Question 30. Given below are two statements. One is labelled as Assertion `A` and the other is labelled as Reason `R`.

Assertion `A` : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height `h_1` and `h_2` respectively, then `R=4\sqrt{h_1h_2}`

Reason `R` : Product of said heights.
`h_1h_2=({u^2sin^2\theta}/{2g}).({u^2cos^2\theta}/{2g})`

Choose the correct answer :

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is NOT the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

Answer (a)


Question 31. Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by `X_p(t)=\alphat+\betat^2` and `X_Q(t)=ft-t^2`. At what time, both the buses have same velocity?

(a) `{\alpha-f}/{1+\beta}`

(b) `{\alpha+f}/{2(\beta-1)}`

(c) `{\alpha+f}/{2(1+\beta)}`

(d) `{f-\alpha}/{2(1+\beta)}`

Answer (d)


Question 32. A projectile is projected with velocity of `25 m/s` at an angle `\theta`  with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of `\theta` will be :

[use `g = 10 m/s^2`]

(a) `1/2sin^-1({5t^2}/{4R})`

(b) `1/2sin^-1({4R}/{5t^2})`

(c) `tan^-1({4t^2}/{5R})`

(d) `Cot^-1({R}/{20t^2})`

Answer (d)

Sep-2021

Question 33. The ranges and heights for two projectiles projected with the same initial velocity at angles `42^o` and `48^o` with the horizontal are `R_1, R_2` and `H_1, H_2` respectively. Choose the correct option :

(a) `R_1>R_2 and H_1=H_2`
(b) `R_1=R_2 and H_1<H_2`
(c) `R_1<R_2 and H_1<H_2`
(d) `R_1=R_2 and H_1=H_2`
 
Answer (b)

Aug-2021

Question 34. A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

(a) `\sqrt{{2ghu^2+1}/h^2}`

(b) `\sqrt{2ghu^2+h^2}`

(c) `\sqrt{{2gh}/g+h^2}`

(d) `\sqrt{{2gh}/u^2+h^2}`

Answer (c)


Question 35. Water drops are falling from a nozzle of a shower onto the floor, from a height of `9.8 m`. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

(a) `4.18m`
(b) `2.94m`
(c) `2.45m`
(d) `7.35m`

Answer (d)


Question 36. A player kicks a football with an initial speed of `25 ms^-1` at an angle of `45^o` from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take `g = 10 ms^-2`)

(a) `h_{max}=10m,  T=2.5s`
(b)  `h_{max}=15.625m,  T=3.54s`
(c)  `h_{max}=15.625m,  T=1.77s`
(d)  `h_{max}=3.54m,  T=0.125s`

Answer (c)


Question 37. A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

(a) hyperbola

(b) parabola in the direction of motion of plane

(c) straight line vertically down the plane

(d) parabola in a direction opposite to the motion of plane

Answer (c)

Jul-2021

Question 38. A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching `h/3` in both the directions.

(a) `{\sqrt{2}-1}/{\sqrt{2}+1}`

(b) `{\sqrt{3}-\sqrt{2}}/{\sqrt{3}+\sqrt{2}}`

(c) `{\sqrt{3}-1}/{\sqrt{3}+1}`

(d) `1/3`

Answer (b)


Question 39. The relation between time `t` and distance `x` for a moving body is given as `t = mx^2 + nx`, where m and n are constants. The retardation of the motion is : (When v stands for velocity)

(a) `2mv^3`
(b) `2mnv^3`
(c) `2nv^3`
(d) `2n^2v^3`

Answer (a)


Question 40. A balloon was moving upwards with a uniform velocity of `10 m/s`. An object of finite mass is dropped from the balloon when it was at a height of `75 m` from the ground level. The height of the balloon from the ground when object strikes the ground was around :

(takes the value of `g` as `10 m/s^2`)

(a) `300m`
(b) `200m`
(c) `125m`
(d) `250m`

Answer (c)


Question 41. The instantaneous velocity of a particle moving in a straight line is given as `V=\alphat+\betat^2`, where `\alpha` and `\beta` are constants. The distance travelled by the particle between `1s` and `2s` is :

(a) `3\alpha+7\beta`

(b) `3/2\alpha+7/3\beta`

(c) `\alpha/2+\beta/3`

(d) `3/2\alpha+7/2\beta`

Answer (b)


Question 42. Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at `4^{th}` second after its fall to the next droplet is `34.3 m`. At what rate the droplets are coming from the tap ? (Take `g = 9.8 m/s^2`)

(a) 3 drops/2 sconds
(b) 2 drops/ second
(c) 1 drops/ second
(d) 1 drops/ 7 second

Answer (c)


Question 43. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time `t_1`. If he remains stationary on a moving escalator then the escalator takes him up in time `t_2.` The time taken by him to walk up on the moving escalator will be :

(a) `{t_1t_2}/{t_2-t_1}`

(b) `{t_1+t_2}/2`

(c) `{t_1t_2}/{t_2+t_1}`

(d) `t_2-t_1`

Answer (c)


Question 44. A butterfly is flying with a velocity `4\sqrt{2}m/s` in North-East direction. Wind is slowly blowing at `1 m/s` from North to South. The resultant displacement of the butterfly in `3` seconds is :

(a) `12\sqrt{2}m`
(b) `20m`
(c) `3m`
(d) `15m`

Answer (d)

Mar-2021

Question 45. The velocity - displacement graph of a particle is shown in the figure.

The acceleration- displacement graph of the same particle is represented by :

(a)


(b)


(c)


(d)


Answer (a)



Question 46. The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

(a)

(b)


(c)


(d)


Answer (b)


Question 47. The velocity of a particle is `v = v_0 + g.t + Ft^2`. Its position is `x = 0` at `t = 0`; then its displacement after time (`t = 1`) is :

(a) `V_0+g+f`

(b) `V_0+g/2+f/3`

(c) `V_0+2g+3f`

(d) `V_0+g/2+f`

Answer (b)


Question 48. A rubber ball is released from a height of `5 m` above the floor. It bounces back repeatedly, always rising to `{81}/{100}` of the height through which it falls. Find the average speed of the ball. (Take `g = 10 ms^-2`)

(a) `2.50ms^-1`
(b) `3.0ms^-1`
(c) `2.0ms^-1`
(d) `3.50ms^-1`

Answer (a)

Question 49. A car accelerates from rest at a constant rate `\alpha` for some time after which it decelerates at a constant rate `\beta` to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

(a) `{4\alpha\beta}/{(\alpha+\beta)}t^2`

(b) `{2\alpha\beta}/{(\alpha+\beta)}t^2`

(c) `{\alpha\beta}/{2(\alpha+\beta)}t^2`

(d) `{\alpha\beta}/{4(\alpha+\beta)}t^2`

Answer (c)


Question 50. A mosquito is moving with a velocity `\vec{v}=0.5t^2\hat{i}+3t\hat{j}+9\hat{k} ms^-1` and accelerating in uniform conditions. What will be the direction of mosquito after `2 s`?

(a) `tan^-1(\sqrt{85}/6)` from y-axis

(b) `tan^-1(5/2)` from y-axis

(c) `tan^-1(2/3)` from x-axis

(d) `tan^-1(5/2)` from x-axis

Answer (a)


Question 51. The velocity-displacement graph describing the motion of bicycle is shown in the figure.

The acceleration-displacement graph of the bicycle's motion is best described by :

(a)

(b)

(c)


(d)

Answer (a)

Feb-2021

Question 52. A scooter accelerates from rest for time `t_1` at constant rate `a_1` and then retards at constant rate `a_2` for time `t_2` and comes to rest. The correct value of  `t_1/t_2` wil be :

(a) `{a_1+a_2}/a_2`

(b) `{a_1+a_2}/a_1`

(c) `a_2/a_1`

(d) `a_1/a_2`

Answer (c)


Question 53. The trajectory of a projectile in a vertical plane is `y =\alphax-\betax^2`, where  `\alpha` and `\beta` are constants and `x & y` are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection `\theta` and the maximum height attained H are respectively given by :

(a) `tan^-1\alpha, \alpha^2/{4\beta}`

(b) `tan^-1\alpha, {4\alpha^2}/{\beta}`

(c) `tan^-1(\beta/\alpha), \alpha^2/{\beta}`

(d) `tan^-1\beta, \alpha^2/{2\beta}`

Answer (a)


Question 54. A stone is dropped from the top of a building. When it crosses a point `5 m` below the top, another stone starts to fall from a point `25 m` below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

(a) `50m`
(b) `25m`
(c) `45m`
(d) `35m`

Answer (c)


Question 55. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity `v`. The velocity with which middle point of the train passes the signal post is :

(a) `{u+v}/2`

(b) `\sqrt{{v^2+u^2}/2}`

(c) `{v-u}/2`

(d) `\sqrt{{v^2+u^2}/2}`

Answer (d)


Question 56. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?


(a)

(b)


(c)


(d)



Answer (c)

Sep-2020

Question 57. When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle `60° `from the horizontal. On further increasing the speed of the car to `(1 + \beta)v`, this angle changes to `45^o`. The value of `\beta` is close to :

(a) `0.50`
(b)`0.73`
(c) `0.37`
(d) `0.41`

Answer (b)


Question 58. The velocity `(v)` and time `(t)` graph of a body in a straight line motion is shown in the figure. The point `S` is at `4.333` seconds. The total distance covered by the body in `6 s` is :


(a) `12m`

(b) `11m`

(c) `{49}/4m`

(d) `{37}/3m`

Answer (d)


Question 59. A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to :

[`g` is the acceleration due to gravity]

(a) `t=3.4\sqrt{(h/g)}`

(b) `t=1.8\sqrt{(h/g)}`

(c) `t=\sqrt{{2h}/{3g}}`

(d) `t=2/3\sqrt{(h/g)}`

Answer (a)


Question 60. A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distanced (point B) from A (see figure) sees it at an angle `45^o` with respect to the vertical. When the balloon climbs up a further height `h_2`, it is seen at an angle `60^o` with respect to the vertical if the girl moves further by a distance `2.464` d(point C). Then the height `h_2` is (given tan `30^o = 0.5774`)


(a) `0.464d`
(b) `d`
(c) `0.732d`
(d) `1.464d`

Answer (b)


Question 61. A Tennis ball is released from a height `h` and after freely falling on a wooden floor it rebounds and reaches height `h/2`. The velocity versus height of the ball during its motion may be represented graphically by

(graph are drawn schematically and on not to scale)

(a)

(b)

(c)

(d)

Answer (c)


Question 62. Starting from the origin at time `t = 0`, with initial velocity `5\hat{j}ms^-1` , a particle moves in the x-y plane with a constant acceleration of `(10\hat{i}+4\hat{j}) ms^-2`. At time t, its coordinates are `(20 m, y_0 m)`. The values of `t` and `y_0` are, respectively:

(a) `5s &25m`
(b) `2s & 18m`
(c) `2s & 24m`
(d) `4s & 52m`

Answer (b)



Question 63. Train A and train B are running on parallel tracks in the opposite directions with speeds of `36 km/h` and `72 km/h`, respectively. A person is walking in train A in the direction opposite to its motion with a speed of `1.8 km/ h`. Speed (in `ms^–1`) of this person as observed from train B will be close to :

(take the distance between the tracks as negligible)

(a) `30.5ms^-1`
(b) `29.5ms^-1`
(c) `31.5ms^-1`
(d) `28.5ms^-1`

Answer (b)

Jan-2020

Question 64. A particle starts from the origin at `t = 0` with an

initial velocity of `3.0\hat{i} m/s` and moves in the x-y plane with a constant acceleration `(6\hat{i}+4\hat{j}) ms^-2` . The x-coordinate of the particle at the instant when its y-coordinate is `32 m` is D meters. The value of D is :-

(a) `40`
(b) `32`
(c) `50`
(d) `60`

Answer (d)


Question 65. A particle moves such that its position vector `\vec{r}(t)=cos\omegat\hat{i}+sin\omegat\hat{j}` where `\omega` is a constant and t is time. Then which of the following statements is true for the velocity `\vec{v}(t)` and acceleration `\vec{v}(t)` of the particle :

(a) `\vec{v}` and `\vec{a}` both are perpendicular to `\vec{r}`
(b) `\vec{v}` and `\vec{a}` both are parallel to `\vec{r}`
(c) `\vec{v}` is  perpendicular to `\vec{r}` and `\vec{a}` is directed towards the origin
(d) `\vec{v}` is  perpendicular to `\vec{r}` and `\vec{a}` is directed away from the origin

Answer (c)