Motion Under Gravity

Total Questions: 41

11. The two balls of iron and wood of same weight dropped from the same height in air then - [U.P.P.C.S.(pre) 1992]

(a) they reach the ground at the same time
(b) one falls first another falls later
(c) the wooden balls falls later
(d) they reach the ground after some gap

Correct Answer: (c) the wooden balls falls later

Solution:In the presence of air the iron balls falls first because of the small size and wooden ball falls later because of its larger size.The resistance from air slows sown the fall of the larger thing with same weight. So option (c) will be the correct answer.

12. Two balls A and B are of 10 kg and 1 kg respectively. They are dropped simultaneously from the height of 20 m. which of the following is correct ? [U.P. Lower Sub.(PRE)]

(a) A will reach the the ground first
(b) B will reach the the ground first
(c) Both A and B will reach the ground at the same time
(d) None of the above

Correct Answer: (c) Both A and B will reach the ground at the same time

Solution:Both balls A and B will reach the ground at the same time because both the balls are thrown at the same height of 20 meter.
thus, h=20 m
initial velocity u=0
speed equation for gravitational velocity
v²=u²+2gh
here v²=2gh (u=0)
or v=√2gh
since the height of the balls are equal (h=20) and the formula of final velocity ( v=√2gh ) is not dependent on the ,mass of the balls.thus both balls will reach the ground at the same time.

13. Two objects of the different masses falling near the surface of the moon would ; [69th B.P.S.C. (PRE) 2023]

(a) have different acceleration
(b) undergo a change in their inertia
(c) have same velocity at any instant
(d) experience forces of same magnitude

Correct Answer: (c) have same velocity at any instant

Solution:the question does not give the parameters of height and time.Assuming that the both of the objects are dropped at the same time from the reasonable height they will have the same velocity at any instant as they fall freely near the surface the moon.

14. Assertion (A) :the weight of the human being on the moon is 1/6 in the comparison to earth.reason (R) : The moon does not have gravity like earth. [Chhattisgarh P.C.S.(PRE) 2008]

(a) both (A) and (R) are true but (R) is correct explanation of (A)
(b) both (A) and (R) are true but (R) is not correct explanation of (A)
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.

Correct Answer: (c) (A) is true but (R) is false.

Solution:The moon is the earths only natural satellite.The surface of the moon is only 1/6 that of the earth.So the weight of human being on the moon will be 1/6 of that on the earth. Hence assertion is true but reason is false .

15. The weight of anybody is - [U.P.P.C.S.(MAINS) 2009 , U.P.P.C.S.(pre) 2006]

(a) same at every place on the earth,s surface
(b) maximum at poles
(c) more on equator
(d) more on mountain than in planes

Correct Answer: (b) maximum at poles

Solution:At a given places the value of acceleration due to gravity is constant but it varies from one place to another place on the earth surface due to this fact that earth is not a perfect sphere. It is flattered at the poles and bulges out at the equator.
the polar radius Rp is less than the equatorial radius Re, now
g=GM/R²
Now as G' and M' remain constant therefore
g∝1/R²
thus the value of g' is minimum at equator and maximum at the poles.It means g' increase as we move from the equator to poles.

16. The weight of human body is - [U.P.P.C.S.(mains) 2015]

(a) maximum at the poles
(b) same at every place on the earth
(c) maximum at the equator.
(d) more on the mountain than plans.

Correct Answer: (a) maximum at the poles

17. If the spinning speed of earth increase then the weight of the body at the equator will : [67th B.P.S.C.(PRE)(RE.EXAM) 2022]

(a) increase
(b) decrease
(c) remain constant
(d) be doubled
(e) none of the above/more than one of the above

Correct Answer: (b) decrease

Solution:The weight of a body on the earth is the amount gravitational pull exerted by the earth due to the earth rotations centrifugal force also exerted on a body on earth which tries to move the body away from the centre of the earth.At the equator centrifugal force is maximum as the velocity of rotation is maximum at the equator of the earth.thus at the equator centrifugal force acts against gravity to reduce the weight of the body with the increase in the speed of rotation of the earth the centrifugal force at a equator will increase and the weight of the body will seem to have decreased.

18. The variation of displacement d with time t in the case of a particle falling freely under the gravity from rest is correctly shown in the figure

Correct Answer: (a)

Solution:For an object falling freely from the state of rest under the gravitational acceleration, the equation of motion is
d = 1/2gt², which is also an equation of the parabola and
d∝ t². Therefore option (a) is correct.

19. A smooth plane inclined at an angle θ with the horizontal as shown in the given figure. A body starts from rest and slides down on the inclined surface. The time taken by the body to reach the bottom is-

Correct Answer: (c)

Solution:The body is placed on the smooth plane inclined, thus it moves under g sinθ instead of g and we know that it starts moving from rest, therefore initial speed u = 0
The equation of motion s=ut+1/2gt²

hence l=1/2gsinθ. t² .......(1)

now as we know θ=h/l⇒l=h/sinθ

putting this value of l in equation (1) we get

t² =2*h/gsin²θ

⇒ t=1/sinθ√2h/g

20. A ball is dropped from the top of a high building with a constant acceleration of 9.8 m/s².what will be its velocity after 3 seconds ? [I.A.S. (PRE) 1998]

(a) 9.8 m/s
(b) 16.2 m/s
(c) 29.4 m/s
(d) 39.2 m/s

Correct Answer: (c) 29.4 m/s

Solution:according to equation
a=9.8 m/s² t=3 sec u=0
as we know v=u+at =0+9.8*3=29.4m/s

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Motion Under Gravity