Gravitation PYQs Set 11 (PDF)

Set 11 of 12 · Questions 301-330 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 11 (Q301-330)
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301. $A period of geostationary satellite is$ (1) $30 h$ (2) $24 h$ (3) $48 h$ (4) $12 h$ 302. $Given below are two statements: Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. Statement II: The time period of revolution of the satellite is T = 2 π \frac{R _{e}}{g} (for satellite very close to the earth surface), where R_{e} radius of earth and g acceleration due to gravity. In the light of the above statements, choose the correct answer from the options given below:$ (1) $Both Statement I and Statement II are true$ (2) $Statement I is false but Statement II is true$ (3) $Statement I is true but Statement II is false$ (4) $Both Statement I and Statement II are false$ 303. $Every planet revolves around the sun in an elliptical orbit: (A) The force acting on a planet is inversely proportional to square of distance from sun. (B) Force acting on planet is inversely proportional to product of the masses of the planet and the sun (C) The centripetal force acting on the planet is directed away from the sun. (D) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below:$ (1) $A and D only$ (2) $C and D only$ (3) $B and C only$ (4) $A and C only$ 304. $Choose the correct statement.$ (1) $Acceleration due to gravity increases with increasing altitude.$ (2) $Acceleration due to gravity is independent of mass of earth.$ (3) $A geostationary satellite can have a time period less than 24 h .$ (4) $Acceleration due to gravity decreases with increasing depth assuming earth to be a sphere of uniform density.$ 305. $Find the acceleration of our galaxy, due to the nearest comparably sized galaxy. The approximate masses of each galaxy is 8 \times 10^{11} solar mass and they are separated by 2 million light-years. Each galaxy has a diameter of 100000 light year. (Assume, 1 light year \approx 10^{16} m, gravitational constant, G \approx 10^{- 10} (\frac{Nm ^{2}}{kg ^{2}}) and mass of sun (= 2.0 \times 10^{30} kg)$ (1) $4 \times 10^{- 13} m / s^{2}$ (2) $2 \times 10^{- 13} m / s^{2}$ (3) $5 \times 10^{- 15} m / s^{2}$ (4) $5 \times 10^{- 13} m / s^{2}$ 306. $A planet of mass M, has two natural satellites with masses m_{1} and m_{2} . The radii of their circular orbits are R_{1} and R_{2} respectively. Ignore the gravitational force between the satellites. Define v_{1}, L_{1}, K_{1} and T_{1} to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v_{2}, L_{2}, K_{2} and T_{2} to be the corresponding quantities of satellite 2. Given m_{1} / m_{2} = 2 and R_{1} / R_{2} = 1/4, match the ratios in List-I to the numbers in List-II. List-I P. \frac{v _{1}}{v _{2}} Q. \frac{L _{1}}{L _{2}} R. \frac{K _{1}}{K _{2}} S. \frac{T _{1}}{T _{2}} List-II 1. \frac{1}{8} 2. 1 3. 2 4. 8$ (1) $P \to 4; Q \to 2; R \to 1; S \to 3$ (2) $P \to 3; Q \to 2; R \to 4; S \to 1$ (3) $P \to 2; Q \to 3; R \to 1; S \to 4$ (4) $P \to 2; Q \to 3; R \to 4; S \to 1$ 307. $A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3 \times 1 0^{5} times heavier than the Earth and is at a distance 2.5 \times 1 0^{4} times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is v_{e} = 11.2km s^{-1} . The minimum initial velocity (v_{s}) required for the rocket to be able to leave the Sun-Earth system is closest to: (Ignore the rotation and revolution of the Earth and the presence of any other planet)$ (1) $v_{s} = 72 km s^{-1}$ (2) $v_{s} = 22 km s^{-1}$ (3) $v_{s} = 42 km s^{-1}$ (4) $v_{s} = 62 km s^{-1}$ 308. $Two particles of equal mass 'm' move in a circle of radius 'r' under the action of their mutual gravitational attraction. The speed of each particle will be:$ (1) $\frac{GM}{2 r}$ (2) $\frac{4 GM}{r}$ (3) $\frac{GM}{r}$ (4) $\frac{GM}{4 r}$ 309. $A body of weight W is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:$ (1) $\frac{W}{91}$ (2) $\frac{W}{100}$ (3) $\frac{W}{9}$ (4) $\frac{W}{3}$ 310. $The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be:$ (1) $3 years$ (2) $3 years$ (3) $9 years$ (4) $33 years$ 311. $The orbital period of a geostationary satellite is$ (1) $2 h$ (2) $5 h$ (3) $24 h$ (4) $12 h$ 312. $The escape velocity from earth is 11.2 km / s . If a body is to be projected in a direction making an angle 4 5^{o} to the vertical, then the escape velocity is$ (1) $11.2 \times 2 km / s$ (2) $11.2 km / s$ (3) $11.2/2 km / s$ (4) $11.22 km / s$ 313. $The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v . What will be its total energy?$ (1) $3/4 m v^{2}$ (2) $1/2 m v^{2}$ (3) $m v^{2}$ (4) $-1/2 m v^{2}$ 314. $Let ' g_{h}' and ' g_{d}' be the accelerations due to gravity at height ' h' above the earth's surface and at depth ' d' below the earth's surface respectively. If g_{h} = g_{d} then the relation between ' h' and ' d' is$ (1) $d = h$ (2) $d = \frac{h}{2}$ (3) $d = \frac{h}{4}$ (4) $d = 2 h$ 315. $The masses and radii of the earth and moon are (M_{1}, R_{1}) and (M_{2}, R_{2}) respectively. Their centers are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses:$ (1) $V = \frac{1}{2} \frac{4 G ( M _{1} + M _{2} )}{r}$ (2) $V = \frac{4 G ( M _{1} + M _{2} )}{r}$ (3) $V = \frac{2 G ( M _{1} + M _{2} )}{3 r}$ (4) $V = \frac{2 G ( M _{1} + M _{2} )}{5 r}$ 316. $T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:$ (1) $4$ (2) $2$ (3) $\frac{1}{2}$ (4) $\frac{1}{4}$ 317. $The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be: (Given g = acceleration due to gravity at the surface of earth)$ (1) $g/2$ (2) $g/4$ (3) $g/3$ (4) $g/9$ 318. $The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Re = 6400 km)$ (1) $9.8N$ (2) $4.9N$ (3) $19.6N$ (4) $8N$ 319. $With what velocity should a particle be projected so that its height becomes equal to radius of earth?$ (1) $(\frac{GM}{R})^{1/2}$ (2) $(\frac{8 GM}{R})^{1/2}$ (3) $(\frac{2 GM}{R})^{1/2}$ (4) $(\frac{4 GM}{R})^{1/2}$ 320. $Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The kinetic energy needed to project a body of mass m from earth surface to infinity is \frac{1}{2} mgR, where R is the radius of earth. Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the options given below$ (1) $A is false but R is true$ (2) $Both A and R are true and R is the correct explanation of A$ (3) $A is true but R is false$ (4) $Both A and R are true but R is NOT the correct explanation of A$ 321. $Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by$ (1) (2) (3) (4) 322. $For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. Then escape velocity for this planet will be$ (1) $11.2 km/sec$ (2) $22.4 km/sec$ (3) $5.6 km/sec$ (4) $44.8 km/sec.$ 323. $Potential energy of a body of mass 1 kg free to move along X -axis is given by U (x) = (\frac{x ^{2}}{2} - x) J . If the total mechanical energy of the body is 2 J, then the maximum speed of the body is (Assume only conservative force acts on the body)$ (1) $5 ms^{- 1}$ (2) $5 ms^{- 1}$ (3) $3.5 ms^{- 1}$ (4) $8 ms^{- 1}$ 324. $A mass of 50kg is placed at the centre of a uniform spherical shell of mass 100kg and radius 50m. If the gravitational potential at a point,25m from the center is V kg/m. The value of V is:$ (1) $-60G$ (2) $+2G$ (3) $-20G$ (4) $-4G$ 325. $Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:$ (1) $\frac{1}{2} \frac{GM}{R ( 2 2 + 1 )}$ (2) $\frac{1}{2} \frac{GM}{R} (22 + 1)$ (3) $\frac{1}{2} \frac{GM}{R} (22 - 1)$ (4) $\frac{GM}{R}$ 326. $A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + B x^{2}, is given by$ (1) $Gm (A (\frac{1}{a + L} - \frac{1}{a}) - BL)$ (2) $Gm (A (\frac{1}{a + L} - \frac{1}{a}) + BL)$ (3) $Gm (A (\frac{1}{a} - \frac{1}{a + L}) + BL)$ (4) $Gm (A (\frac{1}{a} - \frac{1}{a + L}) - BL)$ 327. $The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by: (Given R = radius of earth)$ (1) (2) (3) (4) 328. $A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is:$ (1) $\frac{2 GM}{R}$ (2) $\frac{2 GM}{R ^{2}}$ (3) $2 g R^{2}$ (4) $GMR2$ 329. $Three identical particle A, B and C of mass 100 kg each are placed in a straight line with AB = BC = 13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately:$ (1) $21G$ (2) $100G$ (3) $59 G$ (4) $42 G$ 330. $Gravitational force is required for$ (1) $stirring of liquid$ (2) $convection$ (3) $conduction$ (4) $radiation.$