Gravitation PYQs Set 4 (PDF)

Set 4 of 12 · Questions 91-120 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 4 (Q91-120)
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91. $A body of mass m is at height R from the surface of the earth where R is the radius of the earth. If the body is taken from here to a height of 3R from the surface of the earth, the increase in the gravitational potential energy of the body is (g is acceleration due to gravity on the surface of the earth).$ (1) $3 mgR$ (2) $\frac{mgR}{3}$ (3) $4 mgR$ (4) $\frac{mgR}{4}$ 92. $A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ’ m ’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:$ (1) $2 m v^{2}$ (2) $m v^{2}$ (3) $\frac{1}{2} m v^{2}$ (4) $\frac{3}{2} m v^{2}$ 93. $Satellites which give high value data for remote sensing, meteorology and environmental studies are$ (1) $Geostationary satellites$ (2) $Polar satellites$ (3) $Communication satellites$ (4) $Radio satellites$ 94. $Two stars of equal masses M are orbiting in a circle of radius R, their orbital time period is proportional to$ (1) $R^{3/2}$ (2) $R$ (3) $R^{2}$ (4) $R^{1/2}$ 95. $Match the LIST-I with LIST-II List - I A. Gravitational constant B. Gravitational potential energy C. Gravitational potential D. Acceleration due to gravity List - II 1. (LT^{- 2}) II. (L^{2} T^{- 2}) III. (ML^{2} T^{- 2}) IV. (M^{- 1} L^{3} T^{- 2}) Choose the correct answer from the options given below:$ (1) $A-IV, B-III, C-II, D-I$ (2) $A-II, B-IV, C-III, D-I$ (3) $A-I, B-III, C-IV, D-II$ (4) $A-III, B-II, C-I, D-IV$ 96. $In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:$ (1) $10^{39}$ (2) $10^{29}$ (3) $10^{19}$ (4) $10^{36}$ 97. $Two planets, A and B orbit around a star such that time period of A is 8 times the time period of B . The ratio of orbital velocities of the planets A and B is$ (1) $4 : 1$ (2) $1 : 4$ (3) $2 : 1$ (4) $1 : 2$ 98. $A satellite in a circular orbit of radius R has a period of 4 hours. Another satellite with orbital radius 3 R around the same planet will have a period (in hours)$ (1) $16$ (2) $4$ (3) $427$ (4) $48$ 99. $Two spheres of masses m and M are situated in air and the gravitational force between them is F . The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be$ (1) $3 F$ (2) $F$ (3) $F l 3$ (4) $F l 9$ 100. $The escape velocity for a planet whose radius is 1.7 \times 10^{6} m and acceleration due to gravity is 1.7 ms^{- 2} is$ (1) $1.7 kms^{- 1}$ (2) $2.89 kms^{- 1}$ (3) $1.7 2 kms^{- 1}$ (4) $3.4 kms^{- 1}$ 101. $At what height from surface of earth the value of acceleration due to gravity will fall to half that on the surface of the earth?$ (1) $2625 m$ (2) $2625 km$ (3) $2526 m$ (4) $2526 km$ 102. $For a satellite escape velocity is 11 km / s . If the satellite is launched at an angle of 6 0^{o} with the vertical, then escape velocity will be$ (1) $11 km / s$ (2) $113 km / s$ (3) $\frac{11}{3} km / s$ (4) $33 km / s$ 103. $A uniform solid sphere of radius R produces a gravitational acceleration of a_{0} on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes \frac{a _{0}}{4} is$ (1) $4 R$ (2) $3 2 R$ (3) $2 R$ (4) $3 R$ 104. $A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?$ (1) $25$ (2) $50$ (3) $100$ (4) $20$ 105. $For a body projected at an angle with the horizontal from the ground, choose the correct statement,$ (1) $Gravitational potential energy is maximum at the highest point.$ (2) $The horizontal component of velocity is zero at highest point.$ (3) $The vertical component of momentum is maximum at the highest point.$ (4) $The kinetic energy (K.E.) is zero at the highest point of projectile motion.$ 106. $The acceleration due to gravity at a height (1/20) th of the radius of Earth above the Earth's surface is 9 ms^{- 2} . Its value at an equal depth below the surface of earth is$ (1) $9 ms^{- 2}$ (2) $9.25 ms^{- 2}$ (3) $9.5 ms^{- 2}$ (4) $9.8 ms^{- 2}$ 107. $A satellite is moving with a constant speed 'V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is$ (1) $\frac{1}{2} m V^{2}$ (2) $m V^{2}$ (3) $\frac{3}{2} m V^{2}$ (4) $2 m V^{2}$ 108. $Inside a uniform spherical shell: (A) the gravitational field is zero (B) the gravitational potential is zero (C) the gravitational field is same everywhere (D) the gravitation potential is same everywhere (E) all of the above Choose the most appropriate answer from the options given below:$ (1) $(A), (C) and (D) only$ (2) $(E) only$ (3) $(A), (B) and (C) only$ (4) $(B), (C) and (D) only$ 109. $If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g = π^{2} m / s^{2}, then the length of the second's pendulum at a height h = 2 R from the surface of earth will be:$ (1) $\frac{2}{9} m$ (2) $\frac{1}{9} m$ (3) $\frac{4}{9} m$ (4) $\frac{8}{9} m$ 110. $A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use g = \frac{GM}{R ^{2}} = 9.8 ms^{- 2} and radius of earth, R = 6400 km .]$ (1) $49 N$ (2) $49.83 N$ (3) $49.17 N$ (4) $48.83 N$ 111. $Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same center. The work done in this process____J. (Gravitational constant G = 6.7 \times 10^{- 11} N m^{2} / kg^{2})$ (1) $2.85 \times 10^{- 7}$ (2) $4.77 \times 10^{- 7}$ (3) $1.74 \times 10^{- 7}$ (4) $9.86 \times 10^{- 6}$ 112. $Consider a planet whose density is same as that of the earth but whose radius is three times the radius ' R' of the earth. The acceleration due to gravity ' g_{n}' on the surface of planet is g_{n} = x . g where g is acceleration due to gravity on surface of earth. The value of ' x' is$ (1) $9$ (2) $3$ (3) $\frac{1}{3}$ (4) $\frac{1}{9}$ 113. $Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be:$ (1) $\frac{2}{9} F$ (2) $\frac{16}{9} F$ (3) $\frac{8}{9} F$ (4) $F$ 114. $If R_{E} be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is: (Given: r < R_{E})$ (1) $1 - \frac{r}{R _{E}} - \frac{r ^{2}}{R _{E}^{2}} - \frac{r ^{3}}{R _{E}^{3}}$ (2) $1 + \frac{r}{R _{E}} + \frac{r ^{2}}{R _{E}^{2}} + \frac{r ^{3}}{R _{E}^{3}}$ (3) $1 + \frac{r}{R _{E}} - \frac{r ^{2}}{R _{E}^{2}} + \frac{r ^{3}}{R _{E}^{3}}$ (4) $1 + \frac{r}{R _{E}} - \frac{r ^{2}}{R _{E}^{2}} - \frac{r ^{3}}{R _{E}^{3}}$ 115. $A space station is at a height equal to the radius of the Earth. If v_{E} is the escape velocity on the surface of the Earth, the same on the space station is times v_{E} .$ (1) $\frac{1}{2}$ (2) $\frac{1}{4}$ (3) $\frac{1}{2}$ (4) $\frac{1}{3}$ 116. $The radius of the earth and the radius of orbit around the Sun are 6371 km and 149 \times 1 0^{6} km respectively. The order of magnitude of the diameter of the orbit is greater than that of Earth by$ (1) $10^{3}$ (2) $10^{4}$ (3) $10^{2}$ (4) $10^{5}$ 117. $If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately: (Take: g = 10 ms^{- 2}, the radius of earth, R = 6400 \times 10^{3} m, Take π = 3.14)$ (1) $60 minutes$ (2) $does not change$ (3) $1200 minutes$ (4) $84 minutes$ 118. $Acceleration due to gravity on the surface of earth is ' g '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ......g.$ 119. $An asteroid is moving directly towards the centre of the earth. when at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km / s . Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km / s^{- 1}) ? Give your answer to the nearest integer in kilometer/s$ 120. $The radius in kilometer to which the present radius of earth R = 6400 km to be compressed so that theescape velocity is increased 10 time is$