free fall, mass and weight 9th class (lec 2)

 video lecture for free fall, mass, and weight

Question 1: Two objects of different masses falling freely near the surface of moon would (a) have same velocities at any instant (b) have different accelerations (c) experience forces of same magnitude (d) undergo a change in their inertia Question 2: The value of acceleration due to gravity

(a) is same on equator and pole? (b) is least on poles (c) is least on equator (d) increases from pole to equator

Question 3: The weight of an object at the centre of the earth of radius `R` is

(a) zero

(b) infinite

(c) `R` times the weight at the surface of the earth

(d) `1/R^{2}` times the weight at surface of the earth

Question 4: On the earth, a stone is thrown from a height in a direction parallel to the earth’s surface while another stone is simultaneously dropped from the same height. Which stone would reach the ground first and why?

Question 5: Identical packets are dropped from two aeroplanes, one above the equator and the other above the north pole, both at height h. Assuming all conditions are identical, will those packets take same time to reach the surface of earth. Justify your answer.

Question 6: Two objects of masses `m_{1}`, and `m_{2}` having the same size are dropped simultaneously from heights `h_{1}`, and `h_{2}` respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if

(i) one of the objects is hollow and the other one is solid and

(ii) both of them are hollow, size remaining the same in each case. Give reason.

Question 7: Define free fall

Question 8: When does a body experience a free fall?

Question 9: On Mount Everest, the value of the acceleration due to gravity is __________ than its value in Kashmir Valley.

Question 10: Calculate the acceleration due to gravity on a planet of mass `2\times10^{27} kg` and radius `14\times10^{7} m`. a) `25.2ms^{-2}` b) `27.2ms^{-2}` c) `27.2ms^{2}` d) `24.2ms^{-2}`

Question 11: The mass of moon is `7.3\times10^{22} kg` and its radius is 

`1.74\times10^{6} m`. Find the value of the acceleration due 

to gravity on the moon.

a) `1.62Nkg^{-1}`.

b) `2Nkg^{-1}`

c) `2.62Nkg^{-1}`

d) `1.62N`

Question 12: The place where the value of ‘g’ is unaffected by the

increase (or) decrease in the speed of rotation of the

Earth about its own axis is

(a) equator.               

(b) poles.

(c) tropic of Cancer   

(d) tropic of Capricorn.

Question 13: A cone and a cylinder having same base area and

height are placed on a horizontal surface. What is the

ratio of the heights of centre of gravity of the cone

and the cylinder from the surface?

(a) `5 : 3`  

(b) `3 : 5`

(c) `3 : 2`  

(d) `1 : 2`

Question 14: The weight of a body of mass `3 kg` at the centre of

the Earth is _____.

(a) `9.75 N`   

(b) `1.46 N`

(c)  `zero`               

(d) `4.36 N`

Question 15:  Acceleration due to gravity of a body is independent

of

(a) mass of the body.

(b) altitude of the body.

(c) latitude of the body.

(d) depth below the Earth’s surface.

Question 16:  If the ratio of the masses of two planets is 2 : 3 and

the ratio of their radii are 4 : 7, then the inverse ratio

of their accelerations due to gravity will be _____.

(a) `49 : 24`  

(b) `7 : 8`

(c) `24 : 49`   

(d) `8 : 7`

Question 17: As it falls, the acceleration of a body dropped from

the height equal to that of radius of earth,

(a) remains the same.

(b) decreases.

(c) increases.

(d) initially increases then decreases

Question 18: If the acceleration due to gravity at a height `‘h’` from

the surface of the Earth is `96%` less than its value on

the surface, then `h = _____R` where `R` is the radius

of the Earth.

(a) `1`  

(b) `2`  

(c) `3`   

(d) `4`

Answer Key

Q1:  Solution:

(a) For the two /objects, of different masses falling freely near the surface of moon,

`u = 0` and `a = g_{m}`

`v = u + at =g_{m}t`

At any instant of time, both will have same velocity.

Q2:  Solution:

(c) Acceleration due to gravity, `g=G\frac{M}{R^{2}}`

As the radius of the earth is smaller at the poles as compared to the equator, the value of `g` is greater at the poles and is least on equator.

Q3:  Acceleration due to gravity (g) is zero at the centre of earth. Therefore the weight of an object at the centre of earth `= mg = m\times0 = 0`

Q4:   Solution:

A stone is thrown from a height in a direction parallel to earth’s surface, i.e., the stone is given initial velocity in the horizontal direction. For vertical motion of the stone, `u = 0, a – g` and `s = h` Using `s=ut+\frac{1}{2}at^{2}` we get `t=\sqrt{\frac{2h}{g}}` Similarly, for the second stone, vertical motion is same as that of first. So, both the stones would reach the ground simultaneously.

Q5:  The value of acceleration due to gravity is greater at the poles than at the equator. So, the packet dropped at north pole from a height h, will accelerate more than the packet dropped at equator from the same height and hence will reach the surface of earth earlier.

Q6:   Solution:

For the object of mass m1dropped from hight `h_{1},u=0, a=g, s=h_{1}`

Using `s=ut+\frac{1}{2}at^{2}`, we get `h_{1}=0+\frac{1}{2}g\timest^{2}` Or `t_{1}=\sqrt{\frac{2h_{1}}{g}}` Similarly for the object of mass m2dropped from hight `h_{2}`, `t_{2}=\sqrt{\frac{2h_{2}}{g}}` `\frac{t_{1}}{t_{2}}=\sqrt{\frac{2h_{1}}{g}}\times\sqrt{\frac{2h_{2}}{g}}=\sqrt{\frac{h_{1}}{h_{2}}}` Yes, the ratio remains the same in both the cases as this ratio is independent of mass and size of the objects.

Q7:    A situation in which an object moves only under the influence of gravity.

Q8:  Any object that is being acted upon only by the force of gravity is said to be in a state of free fall.

Q9:   less

Q10:   (b),  Q11:  (a),   Q12:   (b),  Q13:   (d),  Q14:   (c),  Q15:   (a),  Q16:   (c),  Q17:   (c),

Q18:   (d)