Gravitation PYQs Set 12 (PDF)

Set 12 of 12 · Questions 331-351 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 12 (Q331-351)
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331. $The masses and radii of the earth and moon are (M_{1}, R_{1}) and (M_{2}, R_{2}) respectively. Their centers are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses:$ (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) $V = \frac{2 G ( M _{1} + M _{2} )}{5 r}$ 332. $Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are):$ (1) $The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is .$ (2) $The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is .$ (3) $The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is .$ (4) $The energy of the mass m remains constant.$ 333. $T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:$ (1) $4$ (2) $2$ (3) $\frac{1}{2}$ (4) $\frac{1}{4}$ 334. $The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be: (Given g = acceleration due to gravity at the surface of earth)$ (1) $g/2$ (2) $g/4$ (3) $g/3$ (4) $g/9$ 335. $The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Re = 6400 km)$ (1) $9.8N$ (2) $4.9N$ (3) $19.6N$ (4) $8N$ 336. $With what velocity should a particle be projected so that its height becomes equal to radius of earth?$ (1) $(\frac{GM}{R})^{1/2}$ (2) $(\frac{8 GM}{R})^{1/2}$ (3) $(\frac{2 GM}{R})^{1/2}$ (4) $(\frac{4 GM}{R})^{1/2}$ 337. $Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The kinetic energy needed to project a body of mass m from earth surface to infinity is \frac{1}{2} mgR, where R is the radius of earth. Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the options given below$ (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) $Both A and R are true but R is NOT the correct explanation of A$ 338. $Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by$ (1) (2) (3) (4) 339. $For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. Then escape velocity for this planet will be$ (1) $11.2 km/sec$ (2) $22.4 km/sec$ (3) $5.6 km/sec$ (4) $44.8 km/sec.$ 340. $Potential energy of a body of mass 1 kg free to move along X -axis is given by U (x) = (\frac{x ^{2}}{2} - x) J . If the total mechanical energy of the body is 2 J, then the maximum speed of the body is (Assume only conservative force acts on the body)$ (1) $5 ms^{- 1}$ (2) $5 ms^{- 1}$ (3) $3.5 ms^{- 1}$ (4) $8 ms^{- 1}$ 341. $A mass of 50kg is placed at the centre of a uniform spherical shell of mass 100kg and radius 50m. If the gravitational potential at a point,25m from the center is V kg/m. The value of V is:$ (1) $-60G$ (2) $+2G$ (3) $-20G$ (4) $-4G$ 342. $Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:$ (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) $\frac{GM}{R}$ 343. $A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + B x^{2}, is given by$ (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) $Gm (A (\frac{1}{a} - \frac{1}{a + L}) - BL)$ 344. $The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by: (Given R = radius of earth)$ (1) (2) (3) (4) 345. $A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is:$ (1) $\frac{2 GM}{R}$ (2) $\frac{2 GM}{R ^{2}}$ (3) $2 g R^{2}$ (4) $GMR2$ 346. $Three identical particle A, B and C of mass 100 kg each are placed in a straight line with AB = BC = 13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately:$ (1) $21G$ (2) $100G$ (3) $59 G$ (4) $42 G$ 347. $Gravitational force is required for$ (1) $stirring of liquid$ (2) $convection$ (3) $conduction$ (4) $radiation.$ 348. $(1) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius. (3) To evaluate the gravitational field intensity due to anybody at an external point, the entire mass of the body can be considered to be concentrated at its C.G. (4) The radius of gyration of anybody rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis. Which one of the following pairs of statements is correct?$ (1) $(4) and (1)$ (2) $(1) and (2)$ (3) $(2) and (3)$ (4) $(3) and (4)$ 349. $A body of mass (2M) splits into four masses {m, M-m, m, M-m}, which are rearranged to form a square as shown in the figure. The ratio of \frac{M}{m} for which, the gravitational potential energy of the system becomes maximum is x:1. The value of x is$ 350. $Two satellites S_{1} and S_{2} are revolving in circular orbits around a planet with radius R_{1} = 3200 km and R_{2} = 800 km respectively. The ratio of speed of satellite Si to the speed of satellite S_{2} in their respective orbits would be \frac{1}{x} where x =$ 351. $The elongation of a wire on the surface of the earth is 1 0^{- 4} m. The same wire of same dimensions is elongated by 6 x 1 0^{- 5} m on another planet. The acceleration due to gravity on the planet will be............ m s^{- 1} . (Take acceleration due to gravity on the surface of earth =10m/ s^{- 2})$