Gravitation PYQs Set 9 (PDF)

Set 9 of 12 · Questions 241-270 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 9 (Q241-270)
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241. $The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L . Themagnitude of the areal velocity of the planet is:$ (1) $\frac{4 L}{M}$ (2) $\frac{L}{M}$ (3) $\frac{2 L}{M}$ (4) $\frac{L}{2 M}$ 242. $A particle of mass M is situated at the centre of a spherical shell of same mass and radius a . The magnitude of the gravitational potential at a point situated at a l 2 distance from the center, will be$ (1) $\frac{GM}{a}$ (2) $\frac{2 GM}{a}$ (3) $\frac{3 GM}{a}$ (4) $\frac{4 GM}{a}$ 243. $Two bodies of mass m and 9 m are placed at a distance R . The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) [NEET 2023]$ (1) $- \frac{12 Gm}{R}$ (2) $- \frac{16 Gm}{R}$ (3) $- \frac{20 Gm}{R}$ (4) $- \frac{8 Gm}{R}$ 244. $A planet of mass m moves in a elliptical orbit around an unknown star of mass M such that its maximum and minimum distances from the star are equal to r_{1} and r_{2} respectively. The angular momentum of the planet relative to the centre of the star is$ (1) $m \frac{2 GM r _{1} r _{2}}{r _{1} + r _{2}}$ (2) $0$ (3) $m \frac{2 GM ( r _{1} + r _{2} )}{r _{1} r _{2}}$ (4) $\frac{2 GMm r _{1}}{( r _{1} + r _{2} ) r _{2}}$ 245. $Aman o f 50 k g mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m / s . When the stone reaches the floor, the distance of the man above the floor will be$ (1) $9.9 m$ (2) $10.1 m$ (3) $10 m$ (4) $20 m$ 246. $A small point of mass m is placed at a distance 2 R from the centre ' O' of a big uniform solid sphere of mass M and radius R. The gravitational force on ' m ' due to M is F_{1} . A spherical part of radius R /3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F_{2} . The value of ratio F_{1} : F_{2} is$ (1) $12 : 11$ (2) $11 : 10$ (3) $12 : 9$ (4) $16 : 9$ 247. $Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the center of square. The total gravitational potential energy of the system is:$ (1) $- \frac{G m}{d} [(4 + 2) m + 42 M]$ (2) $- \frac{G m}{d} [(4 + 2) m + 42 m]$ (3) $- \frac{G m}{d} [3 m^{2} + 42 M]$ (4) $- \frac{G m}{d} [6 m^{2} + 42 M]$ 248. $The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_{A}, K_{B} and K_{C}, respectively. AC is the major axis and SB is perpendicular to AB at the position of the Sun S as shown in the figure. Then$ (1) $K_{A} < K_{B} < K_{C}$ (2) $K_{B} > K_{A} > K_{C}$ (3) $K_{B} < K_{A} < K_{C}$ (4) $K_{A} > K_{B} > K_{C}$ 249. $A body of mass m is placed on earth’s surface which is taken from earth surface to a height of h = 3 R, then change in gravitational potential energy is$ (1) $\frac{m g R}{4}$ (2) $\frac{2}{3} m g R$ (3) $\frac{3}{4} m g R$ (4) $\frac{m g R}{2}$ 250. $A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is:$ (1) $\frac{2 GM}{7 R} (42 - 5)$ (2) $- \frac{2 GM}{7 R} (42 - 5)$ (3) $\frac{GM}{4 R}$ (4) $\frac{2 GM}{5 R} (2 - 1)$ 251. $A body of mass m is projected with velocity λ ve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ < 1. If air resistance is considered to the negligible, then the maximum height from the center of earth, to which the body can go, will be (R: radius of earth)$ (1) $\frac{R}{1 + λ ^{2}}$ (2) $\frac{R}{1 - λ ^{2}}$ (3) $\frac{R}{1 - λ}$ (4) $\frac{λ ^{2} R}{1 - λ ^{2}}$ 252. $The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:$ (1) $200 N$ (2) $Zero$ (3) $100 N$ (4) $300 N$ 253. $Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, ........ respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:$ (1) $- \frac{8}{3} G$ (2) $- \frac{4}{3} G$ (3) $-4G$ (4) $-G$ 254. $Two identical particles each of mass m go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each particle will be:$ (1) $\frac{Gm}{a ^{3}}$ (2) $\frac{Gm}{8 a ^{3}}$ (3) $\frac{Gm}{4 a ^{3}}$ (4) $\frac{Gm}{2 a ^{3}}$ 255. $Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d = \frac{R}{2} from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given R = radius of earth)$ (1) $300 N$ (2) $100 N$ (3) $400 N$ (4) $500 N$ 256. $A particle of mass M is situated at the center of a spherical shell of same mass and radius a. The gravitational potential at a point situated at \frac{a}{2} distance from the center, will be$ (1) $- \frac{3 GM}{a}$ (2) $- \frac{2 GM}{a}$ (3) $- \frac{GM}{a}$ (4) $- \frac{4 GM}{a}$ 257. $Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be$ (1) $Speed$ (2) $Kinetic energy$ (3) $Total energy$ (4) $Potential energy$ 258. $The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is [NEET 2019]$ (1) $2 mgR$ (2) $\frac{1}{2} mgR$ (3) $\frac{3}{2} mgR$ (4) $mgR$ 259. $A planet having mass 9 M_{e} and radius 4 R_{e}, where M_{e} and R_{e} are mass and radius of earth respectively, has escape velocity in km s^{- 1} given by: (Given escape velocity on earth V_{e} = 11. 2 x 1 0^{3} m s^{- 1})$ (1) $67.2$ (2) $16.8$ (3) $11.2$ (4) $33.6$ 260. $The bodies of masses 100 kg and 8100 kg are held at a distance of 1 m . The gravitational field at a point on the line joining them is zero. The gravitational potential at that point in J / kg is (G = 6.67 \times 10^{- 11} Nm^{2} / kg^{2})$ (1) $- 6.67 \times 10^{- 7}$ (2) $- 6.67 \times 10^{- 10}$ (3) $- 13.34 \times 10^{- 7}$ (4) $- 6.67 \times 10^{- 9}$ 261. $A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be: (Take radius of earth = 6400 km and g=10 m s^{- 2})$ (1) $800km$ (2) $1600km$ (3) $2133 km$ (4) $4800 km$ 262. $The earth (mass = 6 \times 1 0^{24} k g) revolves around the sun with an angular velocity of 2 \times 1 0^{- 7} r a d / s in a circular orbit of radius 1.5 \times 1 0^{8} km. The force exerted by the sun on the earth, in newton, is$ (1) $36 \times 1 0^{21}$ (2) $27 \times 1 0^{39}$ (3) $zero$ (4) $18 \times 1 0^{25}$ 263. $Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is (\frac{2 2 + 1}{32}) \frac{Gm ^{2}}{L ^{2}}, the length of the sides of the square is$ (1) $\frac{L}{2}$ (2) $4 L$ (3) $3 L$ (4) $2 L$ 264. $Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:$ (1) $zero$ (2) $- \frac{4 Gm}{r}$ (3) $- \frac{6 Gm}{r}$ (4) $- \frac{9 Gm}{r}$ 265. $A solid sphere of radius R gravitationally attracts a particle placed at R from its centre with a force F_{1} . Now a spherical cavity of radius (\frac{R}{2}) is made in the sphere (as shown in figure) and the force becomes F_{2} .. The value of F_{1} : F_{2} is$ (1) $41 : 50$ (2) $36 : 25$ (3) $50 : 41$ (4) $25 : 36$ 266. $Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately) (take g = 10 m s^{- 2}, radius of earth = 6400 km)$ (1) $24 hours$ (2) $1 hour 24 minutes$ (3) $1 hour 40 minutes$ (4) $12 hours$ 267. $Kepler's second law (law of areas) is nothing but a statement of$ (1) $work-energy theory$ (2) $conservation of linear momentum$ (3) $conservation of angular momentum$ (4) $conservation of energy$ 268. $A ring has a mass M and radius R . The distance of the point on its geometric axis from its center at which the gravitational field is strongest is$ (1) $\frac{R}{2}$ (2) $\frac{R}{4}$ (3) $\frac{R}{3}$ (4) $\frac{R}{2}$ 269. $A planet is revolving around the sun in which of the following is correct statement?$ (1) $The time taken in travelling DAB is less than that for BCD.$ (2) $The time taken in travelling DAB is greater than that for BCD.$ (3) $The time taken in travelling CDA is less than that for ABC.$ (4) $The time taken in travelling CDA is greater than that for ABC$ 270. $From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure. Taking gravitational potential V = 0 at r = \infty, the potential at the center of the cavity thus formed is :(G = gravitational constant)$ (1) $\frac{- GM}{2 R}$ (2) $\frac{- GM}{R}$ (3) $\frac{- 2 GM}{3 R}$ (4) $\frac{- 2 GM}{R}$