Gravitation PYQs Set 3 (PDF)

Set 3 of 12 · Questions 61-90 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 3 (Q61-90)
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61. $The time period of a satellite in a circular orbit of radius R is T . The period of another satellite in a circular orbit of radius 9 R is:$ (1) $9 T$ (2) $27 T$ (3) $12 T$ (4) $3 T$ 62. $The value of gravitational acceleration g at a height h above the earth's surface is \frac{g}{4} then (R = radius of earth)$ (1) $h = R$ (2) $h = \frac{R}{2}$ (3) $h = \frac{R}{3}$ (4) $h = \frac{R}{4}$ 63. $A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02R. The percentage difference in the time periods of the two satellites is:$ (1) $1.5$ (2) $2.0$ (3) $0.7$ (4) $3.0$ 64. $What will be the formula of mass of the earth in terms of g, R and G ?$ (1) $G \frac{R}{g}$ (2) $g \frac{R ^{2}}{G}$ (3) $g^{2} \frac{R}{G}$ (4) $G \frac{g}{R} .$ 65. $The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is (R = radius of the earth)$ (1) $\frac{2 ( R + h )}{R}$ (2) $\frac{R + h}{2 R}$ (3) $\frac{R + h}{R}$ (4) $\frac{R}{R + h}$ 66. $Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R /4 depth under surface of earth?$ (1) $75 N$ (2) $300 N$ (3) $375 N$ (4) $225 N$ 67. $Consider a binary star system of star A and star B with masses m_{A} and m_{B} revolving in a circular orbit of radii r_{A} and r_{B}, respectively. If T_{A} and T_{B} are the time period of star A and B, respectively, then:$ (1) $\frac{T _{A}}{T _{B}} = (\frac{r _{A}}{r _{B}})^{3/2}$ (2) $T_{A} = T_{B}$ (3) $T_{A} > T_{B} (if m_{A} > m_{B})$ (4) $T_{A} > T_{B} (if r_{A} > r_{B})$ 68. $The escape speed of an object on the surface of the earth is V . If the object is thrown out with speed 4 V from the surface of the earth, the speed of the object far away from the earth is$ (1) $3 V$ (2) $15 V$ (3) $2.5 V$ (4) $8 V$ 69. $The time period " T " of a satellite is related to the density (ρ) of the planet which is orbiting close around the planet as$ (1) $T \propto ρ^{- 1/2}$ (2) $T \propto ρ^{1/2}$ (3) $T \propto ρ$ (4) $T \propto ρ^{- 3/2}$ 70. $Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initial separation between their centers equal to 12 R . If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is$ (1) $7. 5 R$ (2) $1. 5 R$ (3) $2. 5 R$ (4) $4. 5 R$ 71. $The escape velocities of two planets A and B are in the ratio 1 : 2. If the ratio of their radii respectively is 1 : 3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:$ (1) $\frac{4}{3}$ (2) $\frac{3}{2}$ (3) $\frac{2}{3}$ (4) $\frac{3}{4}$ 72. $Considering earth to be a sphere of radius ' R' having uniform density ' ρ', then value of acceleration due to gravity ' g' in terms of R, ρ and G is$ (1) $g = \frac{3 πR}{ρG}$ (2) $g = \frac{4}{3} πρGR$ (3) $g = \frac{4}{3} πρGR$ (4) $g = \frac{GM}{g R ^{2}}$ 73. $What is a period of revolution of earth satellite? Ignore the height of satellite above the surface of earth. Given: (1) The value of gravitational acceleration g = 10 m s^{- 2} . (2) Radius of earth R_{E} = 6400 km . Take π = 3.14 .$ (1) $83.73 minutes$ (2) $85 minutes$ (3) $90 minutes$ (4) $156 minutes$ 74. $A satellite is revolving round the earth with orbital speed v_{0} . If it stops suddenly, the speed with which it will strike the surface of earth would be (v_{e} = escape velocity of a particle on earth’s surface)$ (1) $\frac{v _{e}^{2}}{v _{0}}$ (2) $v_{0}$ (3) $v_{e}^{2} - v_{0}^{2}$ (4) $v_{e}^{2} - 2 v_{0}^{2}$ 75. $A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is:$ (1) $5$ (2) $10$ (3) $62$ (4) $\frac{6}{2}$ 76. $A projectile is thrown straight upward from the earth's surface with an initial speed V α V_{E} where α is a constant and V_{E} is the escape speed. The projectile travels upto a height 800 km from earth's surface, before it comes to rest. The value of the constant α is (Radius of the earth = 6400 km)$ (1) $\frac{1}{3}$ (2) $\frac{1}{2}$ (3) $\frac{2}{3}$ (4) $\frac{3}{4}$ 77. $The ratio of escape velocity at earth (v_{e}) to the escape velocity at a planet (v_{p}) whose radius and mean density are twice as that of earth is:$ (1) $1 : 2$ (2) $1 : 2$ (3) $1 : 22$ (4) $1 : 4$ 78. $To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is R_{E}, g = acceleration due to gravity on the surface of earth):$ (1) $2 mg R_{E}$ (2) $4 mg R_{E}$ (3) $mg R_{E}$ (4) $1/2 mg R_{E}$ 79. $If v_{e} is escape velocity and v_{o} is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by$ (1) $v_{0^{=}} 2 v_{e}$ (2) $v_{o} = v_{e}$ (3) $v_{e} = 2 v_{0}$ (4) $v_{e} = 2 v_{0}$ 80. $Water fall from a 40 m high dam at the rate of 9 x 1 0^{4} kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100W lamps, that can be lit, is: (Take g = 10 m s^{- 2})$ (1) $25$ (2) $50$ (3) $100$ (4) $18$ 81. $Two planets A and B having masses m_{1} and m_{2} move around the sun in circular orbits of r_{1} and r_{2} radii respectively. If angular momentum of A is L and that of B is 3 L, the ratio of time period (\frac{T _{A}}{T _{B}}) is:$ (1) $(\frac{r _{2}}{r _{1}})^{\frac{3}{2}}$ (2) $\frac{1}{27} (\frac{m _{2}}{m _{1}})^{3}$ (3) $27 (\frac{m _{1}}{m _{2}})^{3}$ (4) $(\frac{r _{1}}{r _{2}})^{3}$ 82. $The escape velocity of a body from the surface of the earth is 11.2 km / s . The escape velocity of a body from a planet having same mean density as the earth but twice the radius of earth is$ (1) $11.2 km / s$ (2) $33.6 km / s$ (3) $5.5 km / s$ (4) $22.4 km / s$ 83. $The height at which the weight of a body becomes 1/ 1 6^{t h}, its weight on the surface of earth (radius R), is$ (1) $5R$ (2) $15R$ (3) $3R$ (4) $4R$ 84. $The time period of a geo-stationary satellite is 24 h, at a height 6 R_{E} (R_{E} is the radius of earth) from surface of earth. The time period of another satellite whose height is 2.5 R_{E} from surface of earth will be [NEET 2019]$ (1) $62 h$ (2) $122 h$ (3) $\frac{24}{25} h$ (4) $\frac{12}{25} h$ 85. $A satellite is in an elliptical orbit around a planet P . It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is$ (1) $1 : 6$ (2) $1 : 2$ (3) $3 : 4$ (4) $1 : 3$ 86. $A geostationary satellite is orbiting around an arbitrary planet ’ P ’ at a height of 11 R above thesurface of ’ P ’, R being the radius of ’ P ’ . The time period of another satellite in hours at a height of 2 R from the surface of ’ P ’ is$ (1) $62$ (2) $\frac{6}{2}$ (3) $3$ (4) $5$ 87. $What is the change in mass of a body, when taken 64 km below the surface of the earth? [take, radius of the earth as 6400 km]$ (1) $Increases by 2 %$ (2) $Remains constant$ (3) $Increases by 1 %$ (4) $Decreases by 1 %$ 88. $A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational force exerted on it will be$ (1) $36 N$ (2) $32 N$ (3) $144 N$ (4) $50 N$ 89. $Two satellite A and B go around a planet in circular orbits having radii 4 R and R respectively. If the speed of A is 3 v, the speed of B will be:$ (1) $3 v$ (2) $6 v$ (3) $4 3 v$ (4) $12 v$ 90. $A body of mass m is at height R from the surface of the earth where R is the radius of the earth. If the body is taken from here to a height of 3R from the surface of the earth, the increase in the gravitational potential energy of the body is (g is acceleration due to gravity on the surface of the earth).$ (1) $3 mgR$ (2) $\frac{mgR}{3}$ (3) $4 mgR$ (4) $\frac{mgR}{4}$