Gravitation PYQs Set 8 (PDF)

Set 8 of 12 · Questions 211-240 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 8 (Q211-240)
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211. $Two particles of masses m and 9 m are separated by a distance r . At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is (G = Universal constant of gravitation)$ (1) $- \frac{4 Gm}{r}$ (2) $- \frac{8 Gm}{r}$ (3) $- \frac{16 Gm}{r}$ (4) $- \frac{32 Gm}{r}$ 212. $A satellite of 10^{3} kg mass is revolving in circular orbit of radius 2 R . If \frac{10 ^{4} R}{6} J energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use g = 10 m / s^{2}, R = radius of earth)$ (1) $2.5 R$ (2) $3 R$ (3) $4 R$ (4) $6 R$ 213. $The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be$ (1) $\frac{3 V}{4}$ (2) $6V$ (3) $12 V$ (4) $\frac{3 V}{2}$ 214. $The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is about 10 times mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be$ (1) $20 N$ (2) $8 N$ (3) $80 N$ (4) $40 N.$ 215. $Correct formula for height of a satellite from earths surface is:$ (1) $(\frac{T ^{2} R ^{2}}{4 π ^{2} g})^{1/3} - R$ (2) $(\frac{T ^{2} R ^{2} g}{4 π ^{2}})^{1/3} - R$ (3) $(\frac{T ^{2} R ^{2} g}{4 π ^{2}})^{- 1/3} + R$ (4) $(\frac{T ^{2} R ^{2} g}{4 π})^{1/2} - R$ 216. $At what height from the surface of earth the gravitation potential and the value of g are - 5.4 \times 1 0^{7} J k g^{- 1} and 6.0 m s^{- 2} respectively? Take the radius of earth as 6400 km.$ (1) $1400 km$ (2) $2000 km$ (3) $2600 km$ (4) $1600 km$ 217. $Two masses 90 kg and 160 kg are separated by a distance of 5 m . The magnitude of intensity of the gravitational field at a point which is at a distance 3 m from the 90 kg mass and 4 m from the 160 kg mass is (Universal gravitational constant, (G = 6.67 \times 10^{- 11} N - m^{2} kg^{- 2})$ (1) $94.3 \times 10^{- 10} N kg^{- 1}$ (2) $9.43 \times 10^{- 10} N kg^{- 1}$ (3) $9.43 \times 10^{- 12} N kg^{- 1}$ (4) $94.3 \times 10^{- 12} N kg^{- 1}$ 218. $Which of the following graphs correctly represents the variation of g on the Earth?$ (1) (2) (3) (4) 219. $The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be$ (1) $2 R$ (2) $4 R$ (3) $\frac{1}{4} R$ (4) $\frac{1}{2} R$ 220. $A planet moving around sun sweeps area A_{1} in 2 days, A_{2} in 3 days and A_{3} in 6 days. Then the relation between A_{1}, A_{2} and A_{3} is$ (1) $3 A_{1} = 2 A_{2} = A_{3}$ (2) $2 A_{1} = 3 A_{2} = 6 A_{3}$ (3) $3 A_{1} = 2 A_{2} = 6 A_{3}$ (4) $6 A_{1} = 3 A_{2} = 2 A_{3}$ 221. $A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points A and B are 90 \times 10^{6} km and 60 \times 10^{6} km, respectively. The ratio of velocities of the planet at the points A and B when its velocities make angle 30^{\circ} and 60^{\circ} with major-axis of the orbit is$ (1) $\frac{3}{2 3}$ (2) $\frac{2}{3}$ (3) $\frac{1}{3}$ (4) $\frac{3}{2}$ 222. $The dependence of acceleration due to gravity g on the distance r from the center of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below The correct figure is$ (1) $(4)$ (2) $(1)$ (3) $(2)$ (4) $(3)$ 223. $Two stars of masses m and 2 m at a distance d rotate about their common centre of mass in free space. The period of revolution is -$ (1) $2 π \frac{d ^{3}}{3 Gm}$ (2) $\frac{1}{2 π} \frac{3 Gm}{d ^{3}}$ (3) $\frac{1}{2 π} \frac{d ^{3}}{3 Gm}$ (4) $2 π \frac{3 Gm}{d ^{3}}$ 224. $A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely in elastically. The speeds of the satellite and the meteorite are the same, Just before the collision. The subsequent motion of the combined body will be$ (1) $such that it escape to infinity$ (2) $In an elliptical orbit$ (3) $in the same circular orbit of radius R$ (4) $in a circular orbit of a different radius$ 225. $The acceleration due to gravity at height h above the earth if h < R (Radius of earth) is given by$ (1) $g ’ = g (1 - \frac{h ^{2}}{2 R ^{2}})$ (2) $g ’ = g (1 - \frac{h}{2 R})$ (3) $g ’ = g (1 - \frac{2 h}{R})$ (4) $g ’ = g (1 - \frac{2 h ^{2}}{R ^{2}})$ 226. $The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B . A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B ?$ (1) $(2/9) m$ (2) $18 m$ (3) $6 m$ (4) $(2/3) m$ 227. $The escape velocity of a planet having mass 6 times and radius 2 times as those of the earth is$ (1) $3 v_{e}$ (2) $3 v_{e}$ (3) $2 v_{e}$ (4) $2 v_{e}$ 228. $An object is taken to a height above the surface of earth at a distance \frac{5}{4} R R from the center of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be$ (1) $36%$ (2) $50%$ (3) $64%$ (4) $25%$ 229. $Net gravitational force at the center of a square is found to be F_{1} when four particles having mass M, 2 M, 3 M and 4 M are placed at the four corners of the square as shown in figure and it is F_{2} when the positions of 3 M and 4 M are interchanged. The ratio \frac{F _{1}}{F _{2}} is \frac{α}{5} . The value of α is____.$ (1) $25$ (2) $3$ (3) $1$ (4) $2$ 230. $The radii of two planets A and B are R and 4R and their densities are ρ and \frac{ρ}{3} respectively. The ratio of acceleration due to gravity at their surfaces (g_{A} : g_{B}) will be$ (1) $4 : 3$ (2) $1 : 16$ (3) $3 : 16$ (4) $3 : 4$ 231. $The acceleration due to gravity at a height1 km above the earth is the same as at a depth d below the surface of earth. Then$ (1) $d = 1 km$ (2) $d = \frac{3}{2} km$ (3) $d = 2 km$ (4) $d = \frac{1}{2} km$ 232. $A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius R_{e} . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become \frac{3}{2} times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R . Value of R is$ (1) $3 R_{e}$ (2) $4 R_{e}$ (3) $2.5 R_{e}$ (4) $2 R_{e}$ 233. $Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. the speed of each particle is:$ (1) $\frac{GM}{R}$ (2) $22 \frac{GM}{R}$ (3) $\frac{GM}{R} (1 + 22)$ (4) $\frac{1}{2} \frac{GM}{R} (1 + 22)$ 234. $Three particles, each of mass M, situated at the vertices of an equilateral triangle of side length ' l'. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation ' l'. The initial speed that should be given to each particle is$ (1) $\frac{2 GM}{l}$ (2) $\frac{GM}{2 l}$ (3) $\frac{GM}{l}$ (4) $\frac{3 GM}{l}$ 235. $A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 \times 10^{6} m above the surface of earth. If earth's radius is 6.38 \times 10^{6} m and g = 9.8 ms^{- 2}, then the orbital speed of the satellite is$ (1) $7.76 kms^{- 1}$ (2) $8.56 kms^{- 1}$ (3) $9.13 kms^{- 1}$ (4) $6.67 kms^{- 1}$ 236. $Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the center of the spherical shell)$ (1) (2) (3) (4) 237. $A particle of mass ‘m’ is kept at rest at a height 3 R from the surface of earth, where R ’ is radius of earth and M is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth) (NEET 2013)$ (1) $(\frac{GM}{2 R})^{1/2}$ (2) $(\frac{g R}{4})^{1/2}$ (3) $(\frac{2 g}{R})^{1/2}$ (4) $(\frac{GM}{R})^{1/2}$ 238. $Two bodies of masses 8 kg are placed at the vertices A and B of an equilateral triangle ABC . A third body of mass 2 kg is placed at the centroid G of the triangle. If AG = BG = CG = 1 m, where should a fourth body of mass 4 kg be placed so that the resultant force on the 2 kg body is zero?$ (1) $At C$ (2) $At a point P on the line CG such that PG = \frac{1}{2} m$ (3) $At a point P on the line CG such that PG = 0.5 m$ (4) $At a point P on the line CG such that PG = 2 m$ 239. $A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. the subsequent motion of the combined body will be:$ (1) $In the same circular orbit of radius R$ (2) $such that it escapes to infinity$ (3) $in an elliptical orbit$ (4) $in a circular orbit of a different radius$ 240. $Choose the incorrect statement from the following: (a) The speed of satellite in a given circular orbit remains constant (b) For a planet revolving around the sun in an elliptical orbit, the total energy of the planet remains constant (c) The linear speed of a planet revolving around the sun remains constant (d) When a body falls towards earth, the displacement of earth towards the body is negligible$