Gravitation PYQs Set 3 (PDF)

Set 3 of 12 · Questions 61-90 of 351

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Mere Teacher · Previous Year Questions JEE Main 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. $A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______\times 10^{10} J . (Mass of earth = 6 \times 10^{24} kg, Radius of earth = 6.4 \times 10^{6} m, Gravitational constant = 6.67 \times 10^{- 11} Nm^{2} kg^{- 2})$