Gravitation PYQs Set 8 (PDF)

Set 8 of 12 · Questions 211-240 of 331

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 8 (Q211-240)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
211. $The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be$ (1) $2 R$ (2) $4 R$ (3) $\frac{1}{4} R$ (4) $\frac{1}{2} R$ 212. $A planet moving around sun sweeps area A_{1} in 2 days, A_{2} in 3 days and A_{3} in 6 days. Then the relation between A_{1}, A_{2} and A_{3} is$ (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) $6 A_{1} = 3 A_{2} = 2 A_{3}$ 213. $A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points A and B are 90 \times 10^{6} km and 60 \times 10^{6} km, respectively. The ratio of velocities of the planet at the points A and B when its velocities make angle 30^{\circ} and 60^{\circ} with major-axis of the orbit is$ (1) $\frac{3}{2 3}$ (2) $\frac{2}{3}$ (3) $\frac{1}{3}$ (4) $\frac{3}{2}$ 214. $The dependence of acceleration due to gravity g on the distance r from the center of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below The correct figure is$ (1) $(4)$ (2) $(1)$ (3) $(2)$ (4) $(3)$ 215. $Two stars of masses m and 2 m at a distance d rotate about their common centre of mass in free space. The period of revolution is -$ (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) $2 π \frac{3 Gm}{d ^{3}}$ 216. $A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely in elastically. The speeds of the satellite and the meteorite are the same, Just before the collision. The subsequent motion of the combined body will be$ (1) $such that it escape to infinity$ (2) $In an elliptical orbit$ (3) $in the same circular orbit of radius R$ (4) $in a circular orbit of a different radius$ 217. $The acceleration due to gravity at height h above the earth if h < R (Radius of earth) is given by$ (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) $g ’ = g (1 - \frac{2 h ^{2}}{R ^{2}})$ 218. $The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B . A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B ?$ (1) $(2/9) m$ (2) $18 m$ (3) $6 m$ (4) $(2/3) m$ 219. $The escape velocity of a planet having mass 6 times and radius 2 times as those of the earth is$ (1) $3 v_{e}$ (2) $3 v_{e}$ (3) $2 v_{e}$ (4) $2 v_{e}$ 220. $An object is taken to a height above the surface of earth at a distance \frac{5}{4} R R from the center of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be$ (1) $36%$ (2) $50%$ (3) $64%$ (4) $25%$ 221. $Net gravitational force at the center of a square is found to be F_{1} when four particles having mass M, 2 M, 3 M and 4 M are placed at the four corners of the square as shown in figure and it is F_{2} when the positions of 3 M and 4 M are interchanged. The ratio \frac{F _{1}}{F _{2}} is \frac{α}{5} . The value of α is____.$ (1) $25$ (2) $3$ (3) $1$ (4) $2$ 222. $The radii of two planets A and B are R and 4R and their densities are ρ and \frac{ρ}{3} respectively. The ratio of acceleration due to gravity at their surfaces (g_{A} : g_{B}) will be$ (1) $4 : 3$ (2) $1 : 16$ (3) $3 : 16$ (4) $3 : 4$ 223. $The acceleration due to gravity at a height1 km above the earth is the same as at a depth d below the surface of earth. Then$ (1) $d = 1 km$ (2) $d = \frac{3}{2} km$ (3) $d = 2 km$ (4) $d = \frac{1}{2} km$ 224. $A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius R_{e} . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become \frac{3}{2} times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R . Value of R is$ (1) $3 R_{e}$ (2) $4 R_{e}$ (3) $2.5 R_{e}$ (4) $2 R_{e}$ 225. $Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. the speed of each particle is:$ (1) $\frac{GM}{R}$ (2) $22 \frac{GM}{R}$ (3) $\frac{GM}{R} (1 + 22)$ (4) $\frac{1}{2} \frac{GM}{R} (1 + 22)$ 226. $Three particles, each of mass M, situated at the vertices of an equilateral triangle of side length ' l'. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation ' l'. The initial speed that should be given to each particle is$ (1) $\frac{2 GM}{l}$ (2) $\frac{GM}{2 l}$ (3) $\frac{GM}{l}$ (4) $\frac{3 GM}{l}$ 227. $A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 \times 10^{6} m above the surface of earth. If earth's radius is 6.38 \times 10^{6} m and g = 9.8 ms^{- 2}, then the orbital speed of the satellite is$ (1) $7.76 kms^{- 1}$ (2) $8.56 kms^{- 1}$ (3) $9.13 kms^{- 1}$ (4) $6.67 kms^{- 1}$ 228. $Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the center of the spherical shell)$ (1) (2) (3) (4) 229. $A particle of mass ‘m’ is kept at rest at a height 3 R from the surface of earth, where R ’ is radius of earth and M is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth) (NEET 2013)$ (1) $(\frac{GM}{2 R})^{1/2}$ (2) $(\frac{g R}{4})^{1/2}$ (3) $(\frac{2 g}{R})^{1/2}$ (4) $(\frac{GM}{R})^{1/2}$ 230. $Two bodies of masses 8 kg are placed at the vertices A and B of an equilateral triangle ABC . A third body of mass 2 kg is placed at the centroid G of the triangle. If AG = BG = CG = 1 m, where should a fourth body of mass 4 kg be placed so that the resultant force on the 2 kg body is zero?$ (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) $At a point P on the line CG such that PG = 2 m$ 231. $A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. the subsequent motion of the combined body will be:$ (1) $In the same circular orbit of radius R$ (2) $such that it escapes to infinity$ (3) $in an elliptical orbit$ (4) $in a circular orbit of a different radius$ 232. $An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M = mass of earth, G = Universal gravitational constant)$ (1) $\frac{3 GM}{R}$ (2) $\frac{2 GM}{R}$ (3) $\frac{GM}{2 R}$ (4) $\frac{GM}{R}$ 233. $A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is S.$ (1) $\frac{R _{e}}{2 g} ((1 + \frac{h}{R _{e}})^{3/2} - 1)$ (2) $\frac{2 R _{e}}{g} ((1 + \frac{h}{R _{e}})^{3/2} - 1)$ (3) $\frac{1}{3} \frac{R _{e}}{2 g} ((1 + \frac{h}{R _{e}})^{3/2} - 1)$ (4) $\frac{1}{3} \frac{2 R _{e}}{g} ((1 + \frac{h}{R _{e}})^{3/2} - 1)$ 234. $The escape velocity of a body on the surface of the earth is 11.2 k m / s . If the earth’s mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes$ (1) $22.4 k m / s$ (2) $44.8 k m / s$ (3) $5.6 k m / s$ (4) $11.2 k m / s .$ 235. $If the gravitational field in the space is given as (- \frac{K}{r ^{2}}) . Taking the reference point to be at r = 2 cm with gravitational potential V = 10 J/kg. Find the gravitational potential at r = 3 cm in SI unit (Given, that K = 6 J cm/kg)$ (1) $9$ (2) $11$ (3) $12$ (4) $10$ 236. $A particle of mass M is situated at the center of spherical shell of same mass M and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the center, will be:$ (1) $\frac{2 GM}{a}$ (2) $\frac{3 GM}{a}$ (3) $\frac{4 GM}{a}$ (4) $\frac{GM}{a}$ 237. $The acceleration due to gravity g and mean density of the earth p are related by which of the following relations? (where G is the gravitational constant and R is the radius of the earth.)$ (1) $p = \frac{3 g}{4 π GR}$ (2) $p = \frac{3 g}{4 π G R ^{3}}$ (3) $p = \frac{4 π g R ^{2}}{3 G}$ (4) $p = \frac{4 π g R ^{3}}{3 G} .$ 238. $Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If T_{A} and T_{B} are the time periods of A and B respectively then the value of T_{B} - T_{A} : [Given: radius of earth = 6400 km, mass of earth (= 6 \times 10^{24} kg)$ (1) $4.24 \times 10^{2} s$ (2) $3.33 \times 10^{2} s$ (3) $1.33 \times 10^{3} s$ (4) $4.24 \times 10^{3} s$ 239. $Starting from the center of the earth having radius r, the variation of g (acceleration due to gravity) is shown by$ (1) (2) (3) (4) 240. $The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be$ (1) $8L$ (2) $9L$ (3) $4L$ (4) $3L$