Gravitation PYQs Set 7 (PDF)

Set 7 of 12 · Questions 181-210 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 7 (Q181-210)
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181. $Consider two satellites S_{1} and S_{2} with periods of revolution 1 hr . and 8 hr . respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S_{1} to the angular velocity of satellite S_{2} is -$ (1) $8 : 1$ (2) $1 : 8$ (3) $2 : 1$ (4) $1 : 4$ 182. $A uniform solid sphere of mass M and radius ' a' is surrounded by a concentric uniform thin spherical shell of mass 0.5 M and radius 1.5 a . The gravitational potential energy of a unit mass kept at a distance of 2.5 a from the center is$ (1) $\frac{- 3 GM}{5 a}$ (2) $\frac{3 GM}{5 a}$ (3) $\frac{2 GM}{. 5 a}$ (4) $\frac{- 2 GM}{5 a}$ 183. $On the x -axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by \frac{Ax}{( x ^{2} + a ^{2} ) ^{3/2}} in the x -direction. The magnitude of gravitational potential on the x -axis at a distance x, taking its value to be zero at infinity, is$ (1) $A (x^{2} + a^{2})^{3/2}$ (2) $\frac{A}{( x ^{2} + a ^{2} ) ^{3/2}}$ (3) $\frac{A}{( x ^{2} + a ^{2} ) ^{1/2}}$ (4) $A (x^{2} + a^{2})^{1/2}$ 184. $An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g= 10 m s^{- 2} and radius of earth = 6400 km]$ (1) $48MJ$ (2) $24MJ$ (3) $36MJ$ (4) $12MJ$ 185. $A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the center of the earth? [NEET 2019]$ (1) $200 N$ (2) $250 N$ (3) $100 N$ (4) $150 N$ 186. $Two bodies of masses m_{1} and m_{2} initially at rest at infinite distance apart move towards each other under gravitational force of attraction. Their relative velocity of approach when they are separated by a distance r is (G = universal gravitational constant.)$ (1) $(\frac{2 G ( m _{1} - m _{2} )}{r})^{\frac{1}{2}}$ (2) $(\frac{2 G ( m _{1} + m _{2} )}{r})^{\frac{1}{2}}$ (3) $(\frac{r}{2 G ( m _{1} m _{2} )})^{\frac{1}{2}}$ (4) $(\frac{r}{2 G} m_{1} m_{2})^{\frac{1}{2}}$ 187. $A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98\times 1 0^{24} kg) have to be compressed to be a black hole?$ (1) $1 0^{-9} m$ (2) $1 0^{-6} m$ (3) $1 0^{-2} m$ (4) $100 m$ 188. $A simple pendulum doing small oscillations at a place R height above earth surface has time period of T_{1} = 4 s . T_{2} would be it's time period if it is brought to a point which is at a height 2 R from earth surface. Choose the correct relation [R = radius of earth] :$ (1) $2 T_{1} = T_{2}$ (2) $2 T_{1} = 3 T_{2}$ (3) $T_{1} = T_{2}$ (4) $3 T_{1} = 2 T_{2}$ 189. $The potential energy of a particle in a central field has the form U (r) = \frac{1}{r ^{2}} - \frac{1}{r}, where r is the distance from the center of the field. The magnitude of the maximum attractive force (in N) is$ (1) $\frac{1}{27}$ (2) $\frac{1}{9}$ (3) $\frac{1}{3}$ (4) $1$ 190. $A planet of mass m moves around the Sun along an elliptical path with a period of revolution T . During the motion, the planet's maximum and minimum distance from Sun is R and \frac{R}{3} respectively. If T^{2} = α R^{3}, then the magnitude of constant α will be$ (1) $\frac{10}{9} \cdot \frac{π}{Gm}$ (2) $\frac{20}{27} \cdot \frac{π ^{2}}{Gm}$ (3) $\frac{32}{27} \cdot \frac{π ^{2}}{Gm}$ (4) $\frac{1}{18} \cdot \frac{π ^{2}}{Gm}$ 191. $If g_{E} and g_{m} are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio \frac{Electronic charge on the moon}{electronic charge on the earth} to be$ (1) $1$ (2) $0$ (3) $g_{E} / g_{M}$ (4) $g_{M} / g_{E}$ 192. $The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R_{1} to another of radius R_{2} (R_{2} > R_{1}) is$ (1) $GmM (\frac{1}{R _{1}^{2}} - \frac{1}{R _{2}^{2}})$ (2) $GmM (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ (3) $2 GmM (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ (4) $\frac{1}{2} GmM (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ 193. $The ratio of escape velocity at earth (v_{e}) to the escape velocity at a planet (v_{p}) whose radius and mean density are twice as that of earth is [NEET 2016]$ (1) $1 : 22$ (2) $1 : 4$ (3) $1 : 2$ (4) $1 : 2$ 194. $Periodic time of a satellite revolving above the earth's surface at a height equal to radius of the earth ' R' is [g = acceleration due to gravity]$ (1) $2 π \frac{2 R}{g}$ (2) $4 π \frac{2 R}{g}$ (3) $2 π \frac{R}{g}$ (4) $8 π \frac{R}{g}$ 195. $A body weighs 72 N on the surface of the Earth. What is the gravitational force on it, at a height equal to half of radius of the earth? [NEET 2020]$ (1) $32 N$ (2) $30 N$ (3) $24 N$ (4) $48 N$ 196. $The gravitational potential energy is maximum at$ (1) $infinity$ (2) $the earth's surface$ (3) $the centre of the earth$ (4) $twice the radius of the earth$ 197. $A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,$ (1) $the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant$ (2) $the total mechanical energy of S varies periodically with time$ (3) $the linear momentum of S remains constant in magnitude$ (4) $the acceleration of S is always directed towards the center of the earth$ 198. $A satellite in force free space sweeps stationary interplanetary dust at a rate of \frac{dM}{dt} α v, where M is mass and v is the speed of satellite and α is a constant. The acceleration of satellite is$ (1) $- \frac{α v ^{2}}{2 M}$ (2) $- α v^{2}$ (3) $\frac{- 2 α v ^{2}}{M}$ (4) $- \frac{α v ^{2}}{M}$ 199. $A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one fourth the mass of earth. The radius orbit of planet is: (Given = Radius of geo-stationary orbit for earth is 4.2 \times 10^{4} km)$ (1) $1.4 \times 10^{4} km$ (2) $1.05 \times 10^{4} km$ (3) $8.4 \times 10^{4} km$ (4) $1.68 \times 10^{5} km$ 200. $The ratio of the radii of two planets is ' r' and the ratio of accelerations due to gravity on the planets is ' x'. Then the ratio of the escape velocities from the planets is$ (1) $xr$ (2) $\frac{r}{x}$ (3) $rx$ (4) $\frac{x}{r}$ 201. $The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius r to an orbit of radius \frac{3 r}{2} is$ (1) $66.7$ (2) $50$ (3) $33.33$ (4) $25$ 202. $A thin rod of length ' L' is bent in the form of a circle. Its mass is ' M'. What force will act on mass ' m' placed at the centre of this circle? (G = constant of gravitation)$ (1) $zero$ (2) $\frac{GMm}{4 L ^{2} π ^{2}}$ (3) $\frac{4 π ^{2} GMm}{L}$ (4) $\frac{2 GMm}{L ^{2}}$ 203. $At a certain depth "d" below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R = 6400 km). The depth d is equal to$ (1) $5260 km$ (2) $640 km$ (3) $2560 km$ (4) $4800 km$ 204. $Four particles each of mass m are placed at four vertices of a rectangle having side length as 3 l_{0} and 4 l_{0} . The potential energy of the system in \frac{Gm ^{2}}{l _{o}} is$ (1) $7/6$ (2) $47/30$ (3) $47/60$ (4) $7/12$ 205. $The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius)$ (1) (2) (3) (4) 206. $Two spherical bodies of mass m_{1} and m_{2} have radii 1 m and 2 m respectively. The gravitational field of the two bodies with the radial distance from centre is shown below. The value of \frac{m _{1}}{m _{2}} is$ (1) $\frac{1}{6}$ (2) $\frac{1}{3}$ (3) $\frac{1}{2}$ (4) $\frac{1}{4}$ 207. $Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be$ (1) $\frac{( 1 + 2 2 ) G}{2}$ (2) $G (1 + 22)$ (3) $\frac{G}{2} (22 - 1)$ (4) $\frac{G}{2} (1 + 22)$ 208. $Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4 r respectively around the earth. The ratio of total mechanical energy of A to B is:$ (1) $9 : 16$ (2) $16 : 9$ (3) $1 : 1$ (4) $4 : 3$ 209. $Two planets, A and B are orbiting a common star in circular orbits of radii R_{A} and R_{B}, respectively, with R_{B} = 2 R_{A} . The planet B is 42 times more massive than planet A . The ratio (\frac{L _{B}}{L _{A}}) of angular momentum (L_{B}) of planet B to that of planet A (L_{A}) is closest to integer .$ 210. $Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 x 1 0^{3} km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is \frac{π}{x} r a d h^{- 1} where x is .....$