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Question Bank No: 2

1. The gravitational attraction between the two bodies increases when their masses are

a)		reduced and distance is reduced
b)		increased and distance is reduced
c)		reduced and distance is increased
d)		increased and distance is increased

2. The escape velocity of a body from the surface of earth is 11.2 km/sec.It is thrown up with a velocity 4 times this velocity of escape .The velocity of the body when it has escqped the gravitational pull of earth is

a)		4 $\times 11.2 km / s$
b)		3 $\times 11.2 km / s$
c)		$\sqrt{15}$ $\times 11.2 km / s$
d)		Zero

3. The two planets have radii $r_{1} and r_{2} and their densities p_{1} and p_{2}$ respectively.The ratio of acceleration due to gravity on them will be

a)		$r_{1} p_{1} : r_{2} p_{2}$
b)		$r_{1} {p^{2}}_{1} : r_{2} {p^{2}}_{2}$
c)		${{r^{2}}_{1} p}_{1} : {r^{2}}_{2} p_{2}$
d)		$r_{1} p_{2} : r_{2} p_{1}$

4. The accelaration due to gravity increases by 0.5% when we go from the equator to the poles. What will be the time period of pendulam at the equator which be at a second at the poles?

a)		1.950s
b)		2.050s
c)		1.995s
d)		2.005s

5. If M=mass of earth, R=radius of earth then what is the gravitational potential at distance r=R/2 from its centre

a)		- $\frac{GM}{R}$
b)		- $\frac{3}{2} \frac{GM}{R}$
c)		$\frac{- 8 GM}{11 R}$
d)		$\frac{- 11 GM}{8 R}$

6. An object weights 10 N at the North Pole of the earth .On a geostationary satelite distant 7Rfrom the centre of the earth (of radius R),the true weight and the apparent weight are

a)		0 N, 0 N
b)		0.2 N, 0
c)		0.2N, 9.8N
d)		0.2N,0.2 N

7. Given that the gravitational potential on earth's surface is $v_{0}$ . The potential at a point distance half the radius of earth from the centre will be

a)		$\frac{11 v_{0}}{8}$
b)		$\frac{v_{0}}{2}$
c)		2 $v_{0}$
d)		$\frac{8 v_{0}}{11}$

8. A particle of mass m is placed at the centre of a uniform spherical shell of mass 3m and radius R. The gravitational potential on the surface of the shell is

a)		$- \frac{Gm}{R}$
b)		$- \frac{3 Gm}{R}$
c)		$- \frac{4 Gm}{R}$
d)		$- \frac{2 Gm}{R}$

9. A satellite can be in a geostationary orbit around a planet at a distance r from the centre of the planet. If the angular velocity of the planet about its axis double, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

a)		r / 2
b)		r / $2^{1 / 3}$
c)		r / ${(4)}^{1 / 3}$
d)		r / ${(8)}^{1 / 3}$

10. Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

a)		7.5 R
b)		1.5 R
c)		2.5 R
d)		4.5 R

11. A cosmonaut is orbiting earth in a space craft at an attitude, h = 630 km with a speed of 8 km/s. If the radius of the earth is 6370 km, the acceleration of the cosmonaut is

a)		9.14 m/ $s^{2}$
b)		9.80 m/ $s^{2}$
c)		10.0 m/ $s^{2}$
d)		9.88 m/ $s^{2}$

12. If r represents the radius of the orbit of the satellite of mass m moving around the planet of mass M, then velocity of the satellite v is obtained from the relation

a)		$v^{2} = \frac{GM}{r}$
b)		$v = \frac{GM}{r}$
c)		$v = \frac{Gm}{r}$
d)		$v = \frac{GMm}{r}$

13. Height at which the value of 'g' becomes 1/4 to that on earth is

a)		R
b)		2R
c)		3/2R
d)		4R

14. The metallic bob of a simple pendullum has the relative density $ρ$ . The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by

a)		$\frac{T (ρ - 1)}{ρ}$
b)		$\frac{T ρ}{(ρ - 1)}$
c)		T $\sqrt{\frac{(ρ - 1)}{ρ}}$
d)		T $\sqrt{\frac{(ρ)}{(ρ - 1)}}$

15. A planet is revolving round the sun in an elliptical orbit. The work done on the planet by the gravitational force of sun is zero

a)		in some parts of the orbit
b)		in any part of the orbit
c)		in no part of the orbit
d)		in one complete revolution

16. The ratio of the radius of the earth to that of the moon is 10. The ratio of acceleration due to gravity on the earth and on the moon is 6. The ratio of the escape velocity from the earth's surface to that from the moon is

a)		10
b)		6
c)		nearly 8
d)		1.66

17. The gravitational field due to a mass distributed is E = K/ $x^{3}$ in the x- direction (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x/ $\sqrt{2}$ is

a)		K/ x
b)		K / 2x
c)		K / $x^{2}$
d)		K / 2 $x^{2}$

18. Two spherical planets A and b have same mass but densities in the ratio 8 : 1. For these planets, the acceleration due to gravity at the surface of A to its value at the surface of B is

a)		1 : 4
b)		1 : 2
c)		4 : 1
d)		8 : 1

19. If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is

a)		4 $π$ G/3gR
b)		3 $π$ G/4gR
c)		3g/ 4 $π$ RG
d)		$π$ Rg/12G

20. Rate of change of weight near the earth's surface varies with height as

a)		$h^{- 1}$
b)		$h^{0}$
c)		h
d)		$h^{1 / 2}$

21. A body is projected vertically upwards with a velocity equal to one-third of the escape velocity. What is the maximum height attained by the body?

a)		R
b)		R / 2
c)		R / 4
d)		R / 8

22. The speed of earth's rotation about its axis is w. Its speed is increased to x times to make the effective acceleration due the gravity equal to zero at the equator. Then x is

a)		1
b)		85
c)		17
d)		34

23. A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/ $s^{2}$ , the amount of gas ejected per second to supply the needed thrust will be (g= 10 m/ $s^{2}$ )

a)		127.5 kg/ s
b)		187.5 kg/s
c)		185.5 kg/s
d)		137.5 kg/s

24. If $v_{e}$ is the escape velocity, $v_{0}$ , the orbital velocity and v, the velocity of an object around the earth, then the total mechanical energy of body is +ve when

a)		v < $v_{0}$
b)		v < $v_{e}$
c)		v = $v_{e}$
d)		v > $v_{e}$

25. Let A be area swept out by the line joining the earth and the sun during February 1991. The area swept out by the line during a typical week in February 1991 is

a)		A
b)		2A
c)		4A
d)		$\frac{A}{4}$

26. The mass of the moon is 1/81 times the mass of the earth. The diameter is 1/3.7 times that of the earth. The value of g on the surface of the moon is

a)		6 g
b)		g/6
c)		3g
d)		g/3

27. A hole is bored along the diameter of the earth and a stone is dropped into the hole. The period of oscillation of the stone is

a)		$2 π \sqrt{R / g}$
b)		$2 π \sqrt{Rg}$
c)		$2 π \sqrt{g / R}$
d)		$\frac{1}{2 π} \sqrt{R / g}$

28. If the change in value of 'g' at the height h above the surface of the earth is the same as the change in value at a depth x below it, then

a)		x = h
b)		x = 2h
c)		x = h/2
d)		x = $h^{2}$

29. The acceleration due to gravity on the surface of the earth is 9.8 ${ms}^{- 2}$ . Suppose the earth suddenly shrinks uniformly to half the present size without losing any mass, the value of g in ${ms}^{- 2}$ is

a)		4.9
b)		3.1
c)		39.2
d)		19.6

30. A satellite is moving around the earth in a circular orbit. If R is the radius of the earth and h the height of the satellite from the surface of the earth, the velocity of the satellite is given by

a)		$R$ $\frac{g}{{(R + h)}^{2}}$
b)		$R \sqrt{\frac{R + h}{g}}$
c)		$R^{2} \sqrt{\frac{g}{R + h}}$
d)		$R$ $\sqrt{\frac{g}{R + h}}$

31. The mean radius of the earth is R. Its angular speed on its own axis is $ω$ and the acceleration due to gravity on the surface of the earth is g. The cube of the radius of the orbit of a geostationary satellite is

a)		$R^{2} ω^{2} / g$
b)		$R^{2} g / ω^{2}$
c)		$R^{2} g / ω$
d)		$Rg / ω$

32. What would be the angular speed of earth so that bodies lying on equator may appear weightless? g = 10 ${ms}^{- 2}$ , R = 6, 400 km

a)		$1.25 \times 10^{- 2} rad / s$
b)		$1.25 \times 10^{- 3} rad / s$
c)		$1.25 \times 10^{- 4} rad / s$
d)		$1.25 rad / s$

33. The escape velocity from the surface of the earth is

a)		$\sqrt{8 π Gd R^{2}}$
b)		$\sqrt{\frac{8}{3} G π R^{2} d}$
c)		$\sqrt{\frac{4}{3} G π R^{2} d}$
d)		$4 π RG$

34. The height of a geostationary satellite from the surface of the earth is

a)		36,000 km
b)		30,000 km
c)		20,000 km
d)		26,000 km

35. A planet whose mass is twice and radius also twice that of the earth will have acceleration due to gravity

a)		4.9 ${ms}^{- 2}$
b)		19.6 ${ms}^{- 2}$
c)		9.8 ${ms}^{- 2}$
d)		32 ${ms}^{- 2}$

36. If the radius of the earth were to shrink by 1%, its mass remaining the same. the acceleration due to gravity on the earth's surface would

a)		decrease
b)		increase
c)		remain unchanged
d)		decrease by 1%

37. The value of 'g' at a particular point is 9.8 ${ms}^{- 2}$ . Suppose the earth suddenly shrinks uniformly to half its present size (radius) with out losing any mass. The value of 'g' at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will become

a)		9.8 ${ms}^{- 2}$
b)		4.9 ${ms}^{- 2}$
c)		19.6 ${ms}^{- 2}$
d)		10 ${ms}^{- 2}$

38. The distance of Neptune and Saturn from the sun are nearly $10^{13}$ m and $10^{12}$ m respectively. Assuming that they move in circular orbits, their periods would be in the ratio

a)		10
b)		100
c)		10 $\sqrt{10}$
d)		1,000

39. The weight of a body on the surface of the earth is 90kg wt. If the mass of the moon is 1/9 times that of the earth and the radius is 1/2 that of earth, the weight of the body on the moon is

a)		60 kg wt
b)		50 kg wt
c)		40 kg wt
d)		90 kg wt

40. If V denotes potential difference across the plates of capacitor of capacitance C, the dimension of ${CV}^{2}$ are

a)		Not expressible in terms of M.L.T
b)		${MLT}^{- 2}$
c)		$M^{2} {LT}^{- 1}$
d)		${{ML}^{2} T}^{2}$

41. An experiment measure quantities a, b, and c and x is calculated from $x = \frac{{ab}^{2}}{c^{3}}$ . If the percentage errors in a, b, and c are $\pm 1 %, \pm 3 %$ and $\pm 2 %$ respectively, the percentage error in x can be

a)		$\pm$ 13%
b)		$\pm$ 7%
c)		$\pm$ 4%
d)		$\pm$ 1%

42. A body is thrown vertically upward from the earth with velocity 100 m/s. It will return the earth approximately after

a)		5 Sec
b)		10 Sec
c)		13 Sec
d)		20 Sec

43. The period of Satellite in a circular orbit of radius R is T. What is the period of another satellite in circular orbit of radius 4R?

a)		4T
b)		$\frac{T}{8}$
c)		$\frac{T}{4}$
d)		8T

44. A satellite is revolving round the earth in circular orbit whose radius is R. Work done by the gravitational force in one revolution is

a)		Zero
b)		$2 {mgR}^{2}$
c)		${mgR}^{2}$
d)		$2 mgR$

45. A metallic ball has spherical cavity at its centre. If the ball is heated, what happens to the cavity

a)		Its volume decreases
b)		Its volume remains constant
c)		Its volume decreases, and increases
d)		Its volume increases

46. An earth satellites S has an orbit radius which is 4 times that of a communication satellites C. The period of revolution of S is

a)		2 days
b)		32 days
c)		8 days
d)		16 days

47. A particle is moving eastward with a velocity 5 m/sec. In 10 seconds, the velocity changes to 5 m/s northward. The average acceleration in this time is

a)		$\frac{1}{\sqrt{2}} m / \sec^{2}$ towards northeast
b)		$\frac{1}{\sqrt{2}} m / \sec^{2}$ towards northwest
c)		$\frac{1}{2} m / \sec^{2}$ towards northwest
d)		$\frac{1}{2 \sqrt{2}} m / \sec^{2}$ towards northeastern

48. What is the weight of a 700g of body on a planet whose mass is $\frac{1}{7} th$ of that of earth and radius $\frac{1}{2}$ times of earth?

a)		400gf
b)		300gf
c)		700gf
d)		500gf

49. The escape velocity from the earth's surface is 11.2 Km/s. If a planet has radius twice that of the earth and on which the acceleration due to gravity is twice that on the earth, then escape velocity on this planet will be

a)		11.2 km/s
b)		5.6 km/s
c)		22.4 km/s
d)		33.6 km/s

50. Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity is $V_{A} / V_{B}$

a)		2
b)		$\sqrt{2}$
c)		$1 / \sqrt{2}$
d)		1/2