Gravitation PYQs Set 7 (PDF)

Set 7 of 12 · Questions 181-210 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 7 (Q181-210)
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181. $A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98\times 1 0^{24} kg) have to be compressed to be a black hole?$ (1) $1 0^{-9} m$ (2) $1 0^{-6} m$ (3) $1 0^{-2} m$ (4) $100 m$ 182. $A simple pendulum doing small oscillations at a place R height above earth surface has time period of T_{1} = 4 s . T_{2} would be it's time period if it is brought to a point which is at a height 2 R from earth surface. Choose the correct relation [R = radius of earth] :$ (1) $2 T_{1} = T_{2}$ (2) $2 T_{1} = 3 T_{2}$ (3) $T_{1} = T_{2}$ (4) $3 T_{1} = 2 T_{2}$ 183. $The potential energy of a particle in a central field has the form U (r) = \frac{1}{r ^{2}} - \frac{1}{r}, where r is the distance from the center of the field. The magnitude of the maximum attractive force (in N) is$ (1) $\frac{1}{27}$ (2) $\frac{1}{9}$ (3) $\frac{1}{3}$ (4) $1$ 184. $A planet of mass m moves around the Sun along an elliptical path with a period of revolution T . During the motion, the planet's maximum and minimum distance from Sun is R and \frac{R}{3} respectively. If T^{2} = α R^{3}, then the magnitude of constant α will be$ (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) $\frac{1}{18} \cdot \frac{π ^{2}}{Gm}$ 185. $If g_{E} and g_{m} are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio \frac{Electronic charge on the moon}{electronic charge on the earth} to be$ (1) $1$ (2) $0$ (3) $g_{E} / g_{M}$ (4) $g_{M} / g_{E}$ 186. $The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R_{1} to another of radius R_{2} (R_{2} > R_{1}) is$ (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) $\frac{1}{2} GmM (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ 187. $The ratio of escape velocity at earth (v_{e}) to the escape velocity at a planet (v_{p}) whose radius and mean density are twice as that of earth is [NEET 2016]$ (1) $1 : 22$ (2) $1 : 4$ (3) $1 : 2$ (4) $1 : 2$ 188. $Periodic time of a satellite revolving above the earth's surface at a height equal to radius of the earth ' R' is [g = acceleration due to gravity]$ (1) $2 π \frac{2 R}{g}$ (2) $4 π \frac{2 R}{g}$ (3) $2 π \frac{R}{g}$ (4) $8 π \frac{R}{g}$ 189. $A body weighs 72 N on the surface of the Earth. What is the gravitational force on it, at a height equal to half of radius of the earth? [NEET 2020]$ (1) $32 N$ (2) $30 N$ (3) $24 N$ (4) $48 N$ 190. $The gravitational potential energy is maximum at$ (1) $infinity$ (2) $the earth's surface$ (3) $the centre of the earth$ (4) $twice the radius of the earth$ 191. $A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,$ (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) $the acceleration of S is always directed towards the center of the earth$ 192. $A satellite in force free space sweeps stationary interplanetary dust at a rate of \frac{dM}{dt} α v, where M is mass and v is the speed of satellite and α is a constant. The acceleration of satellite is$ (1) $- \frac{α v ^{2}}{2 M}$ (2) $- α v^{2}$ (3) $\frac{- 2 α v ^{2}}{M}$ (4) $- \frac{α v ^{2}}{M}$ 193. $A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one fourth the mass of earth. The radius orbit of planet is: (Given = Radius of geo-stationary orbit for earth is 4.2 \times 10^{4} km)$ (1) $1.4 \times 10^{4} km$ (2) $1.05 \times 10^{4} km$ (3) $8.4 \times 10^{4} km$ (4) $1.68 \times 10^{5} km$ 194. $The ratio of the radii of two planets is ' r' and the ratio of accelerations due to gravity on the planets is ' x'. Then the ratio of the escape velocities from the planets is$ (1) $xr$ (2) $\frac{r}{x}$ (3) $rx$ (4) $\frac{x}{r}$ 195. $The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius r to an orbit of radius \frac{3 r}{2} is$ (1) $66.7$ (2) $50$ (3) $33.33$ (4) $25$ 196. $A thin rod of length ' L' is bent in the form of a circle. Its mass is ' M'. What force will act on mass ' m' placed at the centre of this circle? (G = constant of gravitation)$ (1) $zero$ (2) $\frac{GMm}{4 L ^{2} π ^{2}}$ (3) $\frac{4 π ^{2} GMm}{L}$ (4) $\frac{2 GMm}{L ^{2}}$ 197. $At a certain depth "d" below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R = 6400 km). The depth d is equal to$ (1) $5260 km$ (2) $640 km$ (3) $2560 km$ (4) $4800 km$ 198. $Four particles each of mass m are placed at four vertices of a rectangle having side length as 3 l_{0} and 4 l_{0} . The potential energy of the system in \frac{Gm ^{2}}{l _{o}} is$ (1) $7/6$ (2) $47/30$ (3) $47/60$ (4) $7/12$ 199. $The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius)$ (1) (2) (3) (4) 200. $Two spherical bodies of mass m_{1} and m_{2} have radii 1 m and 2 m respectively. The gravitational field of the two bodies with the radial distance from centre is shown below. The value of \frac{m _{1}}{m _{2}} is$ (1) $\frac{1}{6}$ (2) $\frac{1}{3}$ (3) $\frac{1}{2}$ (4) $\frac{1}{4}$ 201. $Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be$ (1) $\frac{( 1 + 2 2 ) G}{2}$ (2) $G (1 + 22)$ (3) $\frac{G}{2} (22 - 1)$ (4) $\frac{G}{2} (1 + 22)$ 202. $Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4 r respectively around the earth. The ratio of total mechanical energy of A to B is:$ (1) $9 : 16$ (2) $16 : 9$ (3) $1 : 1$ (4) $4 : 3$ 203. $Two particles of masses m and 9 m are separated by a distance r . At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is (G = Universal constant of gravitation)$ (1) $- \frac{4 Gm}{r}$ (2) $- \frac{8 Gm}{r}$ (3) $- \frac{16 Gm}{r}$ (4) $- \frac{32 Gm}{r}$ 204. $A satellite of 10^{3} kg mass is revolving in circular orbit of radius 2 R . If \frac{10 ^{4} R}{6} J energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use g = 10 m / s^{2}, R = radius of earth)$ (1) $2.5 R$ (2) $3 R$ (3) $4 R$ (4) $6 R$ 205. $The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be$ (1) $\frac{3 V}{4}$ (2) $6V$ (3) $12 V$ (4) $\frac{3 V}{2}$ 206. $The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is about 10 times mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be$ (1) $20 N$ (2) $8 N$ (3) $80 N$ (4) $40 N.$ 207. $Correct formula for height of a satellite from earths surface is:$ (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) $(\frac{T ^{2} R ^{2} g}{4 π})^{1/2} - R$ 208. $At what height from the surface of earth the gravitation potential and the value of g are - 5.4 \times 1 0^{7} J k g^{- 1} and 6.0 m s^{- 2} respectively? Take the radius of earth as 6400 km.$ (1) $1400 km$ (2) $2000 km$ (3) $2600 km$ (4) $1600 km$ 209. $Two masses 90 kg and 160 kg are separated by a distance of 5 m . The magnitude of intensity of the gravitational field at a point which is at a distance 3 m from the 90 kg mass and 4 m from the 160 kg mass is (Universal gravitational constant, (G = 6.67 \times 10^{- 11} N - m^{2} kg^{- 2})$ (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) $94.3 \times 10^{- 12} N kg^{- 1}$ 210. $Which of the following graphs correctly represents the variation of g on the Earth?$ (1) (2) (3) (4)