Gravitation PYQs Set 10 (PDF)

Set 10 of 12 · Questions 271-300 of 331

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Mere Teacher · Previous Year Questions NEET Physics · Gravitation · Set 10 (Q271-300)
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271. $The radius of a planet is twice the radius of earth. Both have almost equal average mass‐ densities. V_{P} and V_{E} are escape velocities of the planet and the earth, respectively, then$ (1) $V_{P} = 1.5 V_{E}$ (2) $V_{P} = 2 V_{E}$ (3) $V_{E} = 3 V_{P}$ (4) $V_{E} = 1.5 V_{P}$ 272. $A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is:$ (1) $\frac{GmM π ^{2}}{L ^{2}}$ (2) $\frac{GMmπ}{2 L ^{2}}$ (3) $0$ (4) $\frac{2 GmMπ}{L ^{2}}$ 273. $The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9. 0 x 1 0^{3} km. Find the mass of Mars. {Given \frac{4 π ^{2}}{G} = 6 \times 1 0^{11} N^{- 1} m^{- 2} kg^{2}}$ (1) $5.96 \times 1 0^{19} k g$ (2) $3.25 \times 1 0^{21} k g$ (3) $7.02 \times 1 0^{25} k g$ (4) $6.00 \times 1 0^{23} k g$ 274. $Two spherical bodies of masses M and 5 M and radii R and 2 R are released in free space with initial separation between their centres equal to 12 R . If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is$ (1) $2.5 R$ (2) $4.5 R$ (3) $7.5 R$ (4) $1.5 R$ 275. $A space ship of mass 2 x 1 0^{4} kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g = 10 m s^{- 2} and radius of earth = 6400 km):$ (1) $11.2 (2 - 1) km s^{- 1}$ (2) $8 (2 - 1) km s^{- 1}$ (3) $7.9 (2 - 1) km s^{- 1}$ (4) $7.4 (2 - 1) km s^{- 1}$ 276. $The escape velocity of a body on a planet 'A' is 12 k m s^{- 1} . The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is:$ (1) $12 k m s^{- 1}$ (2) $24 k m s^{- 1}$ (3) $36 k m s^{- 1}$ (4) $6 k m s^{- 1}$ 277. $A solid sphere of mass ’ M ’ and radius ’ a ’ is surrounded by a uniform concentric spherical shell of thickness 2 M and mass 2 M . The gravitational field at distance ’ 3 a ’ from the center will be:$ (1) $\frac{2 GM}{9 a ^{2}}$ (2) $\frac{GM}{9 a ^{2}}$ (3) $\frac{GM}{3 a ^{2}}$ (4) $\frac{2 GM}{3 a ^{2}}$ 278. $The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_{A}, K_{B} and K_{C}, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure? Then$ (1) $K_{A} < K_{B} < K_{C}$ (2) $K_{A} > K_{B} > K_{C}$ (3) $K_{B} < K_{A} < K_{C}$ (4) $K_{B} > K_{A} > K_{C}$ 279. $A particle of mass m is thrown upwards from the surface of the earth, with a velocity u . The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is$ (1) $\frac{2 GM}{R ^{2}}$ (2) $\frac{2 GM}{R}$ (3) $\frac{2 g M}{R ^{2}}$ (4) $2 g R^{2}$ 280. $If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct? [NEET 2018]$ (1) $Time period of a simple pendulum on the earth would decrease$ (2) $Walking on the ground would become more difficult$ (3) $Raindrops will fall faster$ (4) $g on the earth will not change$ 281. $Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centers. If 8 R is the distance between the centres of a ring (of mass ’ m ’) and a sphere (mass ’ M ’) where both have equal radius ’ R ’ .$ (1) $\frac{8}{9} \cdot \frac{GmM}{R}$ (2) $\frac{8}{27} \cdot \frac{GmM}{R ^{2}}$ (3) $\frac{2 2}{3} \cdot \frac{GMm}{R ^{2}}$ (4) $\frac{1}{3 8} \cdot \frac{GMm}{R ^{2}}$ 282. $At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)$ (1) $5 R - R$ (2) $\frac{3 R - R}{2}$ (3) $\frac{R}{2}$ (4) $\frac{5 R - R}{2}$ 283. $Four identical particles of mass M are located at the corners of a square of side ’ a ’ . What should be their speed if each of them revolves under the influence of others' gravitational field in a circular orbit circumscribing the square?$ (1) $1.35 \frac{GM}{a}$ (2) $1.16 \frac{GM}{a}$ (3) $1.21 \frac{GM}{a}$ (4) $1.41 \frac{GM}{a}$ 284. $Two particles of equal mass ‘m’ go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their center of mass is:$ (1) $\frac{Gm}{4 R}$ (2) $\frac{Gm}{3 R}$ (3) $\frac{Gm}{2 R}$ (4) $\frac{Gm}{R}$ 285. $Consider two solid spheres of radii R_{1} = 1m, R_{2} = 2m and masses M_{1} and M_{2}, respectively. The gravitational field due to sphere (a) and (b) are shown. The value of \frac{M _{1}}{M _{2}} is:$ (1) $\frac{2}{3}$ (2) $\frac{1}{3}$ (3) $\frac{1}{2}$ (4) $\frac{1}{6}$ 286. $The largest and the shortest distance of the earth from the sun are r_{1} and r_{2} . Its distance from the sun when it is at perpendicular to the major‐axis of the orbit drawn from the sun is$ (1) $\frac{r _{1} + r _{2}}{4}$ (2) $\frac{r _{1} + r _{2}}{r _{1} - r _{2}}$ (3) $\frac{2 r _{1} r _{2}}{r _{1} + r _{2}}$ (4) $\frac{r _{1} + r _{2}}{3}$ 287. $A planet revolves round the Sun in an elliptical orbit. The linear speed of the planet will be maximum at$ (1) $D$ (2) $B$ (3) $A$ (4) $C$ 288. $The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below. The correct figure is.$ (1) (2) (3) (4) 289. $The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:$ (1) $64 N$ (2) $25 N$ (3) $50N$ (4) $100 N$ 290. $The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be: (Radius of earth = 6400km)$ (1) $1%$ (2) $3%$ (3) $4%$ (4) $0.5%$ 291. $Infinite number of spheres, each of mass m are placed on the X -axis at distances 1, 2, 4, 8, 16, meters from origin. The magnitude of the gravitational field at the origin is$ (1) $\frac{2}{3} G m$ (2) $\frac{4}{3} G m$ (3) $Gm$ (4) $6 Gm$ 292. $Two planets have masses M and 16 M and their radii are a and 2 a, respectively. The separation between the centres of the planets is 10 a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of smaller planet, the minimum firing speed needed is$ (1) $\frac{3}{2} \frac{5 GM}{a}$ (2) $\frac{GM ^{2}}{ma}$ (3) $2 \frac{GM}{a}$ (4) $4 \frac{GM}{a}$ 293. $Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is$ (1) $\frac{1}{2} \frac{G m}{R}$ (2) $\frac{4 G m}{R}$ (3) $\frac{1}{2 R} \frac{1}{G m}$ (4) $.$ 294. $At some location on earth the horizontal component of earth's magnetic field is 18 \times 10^{- 6} T . At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45^{\circ} angle with horizontal in equilibrium. To keepthis needle horizontal, the vertical force that should beapplied at one of its ends is:$ (1) $3.6 \times 10^{- 5} N$ (2) $1.8 \times 10^{- 5} N$ (3) $1.3 \times 10^{- 5} N$ (4) $6.5 \times 10^{- 5} N$ 295. $A satellite is orbiting just above the surface of the earth with period T . If d is the density of the earth and G is the universal constant of gravitation, the quantity \frac{3 π}{G d} represents$ (1) $T^{2}$ (2) $T^{3}$ (3) $T$ (4) $T$ 296. $At what height from the surface of earth the gravitational potential and the value of g are - 5.4 \times 1 0^{7} J k g^{- 1} and 6.0 m s^{- 2} respectively? Take the radius of earth as 6400 km$ (1) $2000 km$ (2) $2600 km$ (3) $1600 km$ (4) $1400 km$ 297. $Given below are two statements: one is labelled as Assertion (a)and the other is labelled as Reason (R). Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant. Reason (R): For a central force field the angular momentum is a constant. In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $(A) is not correct but (R) is correct$ (2) $Both (A) and (R) are correct but (R) is not the correct explanation of (A)$ (3) $Both (A) and (R) are correct and (R) is the correct explanation of (A)$ (4) $(A) is correct but (R) is not correct$ 298. $At what height from the surface of earth the gravitational potential and the value of g are - 5.4 \times 1 0^{7} J k g^{- 1} and 6.0 m s^{- 2} respectively? Take, the radius of earth as 6400 km. [NEET 2016]$ (1) $1600 km$ (2) $1400 km$ (3) $2000 km$ (4) $2600 km$ 299. $Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and plane i.e. T^{2} = K r^{3} here K is constant If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = \frac{GMm}{r ^{2}}, here G is gravitational constant The relation between G and K is described as:$ (1) $GMK = 4π2$ (2) $K = G$ (3) $K = \frac{1}{G}$ (4) $GK = 4π2$ 300. $Acceleration due to gravity.$ (1) $increases with altitude$ (2) $decreases with altitude$ (3) $is independent of altitude$ (4) $first decrease and then increases with altitude$