Gravitation PYQs Set 11 (PDF)

Set 11 of 12 · Questions 301-330 of 351

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Mere Teacher · Previous Year Questions JEE Main Physics · Gravitation · Set 11 (Q301-330)
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301. $A planet revolves round the Sun in an elliptical orbit. The linear speed of the planet will be maximum at$ (1) $D$ (2) $B$ (3) $A$ (4) $C$ 302. $The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below. The correct figure is.$ (1) (2) (3) (4) 303. $The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:$ (1) $64 N$ (2) $25 N$ (3) $50N$ (4) $100 N$ 304. $The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be: (Radius of earth = 6400km)$ (1) $1%$ (2) $3%$ (3) $4%$ (4) $0.5%$ 305. $Infinite number of spheres, each of mass m are placed on the X -axis at distances 1, 2, 4, 8, 16, meters from origin. The magnitude of the gravitational field at the origin is$ (1) $\frac{2}{3} G m$ (2) $\frac{4}{3} G m$ (3) $Gm$ (4) $6 Gm$ 306. $Two planets have masses M and 16 M and their radii are a and 2 a, respectively. The separation between the centres of the planets is 10 a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of smaller planet, the minimum firing speed needed is$ (1) $\frac{3}{2} \frac{5 GM}{a}$ (2) $\frac{GM ^{2}}{ma}$ (3) $2 \frac{GM}{a}$ (4) $4 \frac{GM}{a}$ 307. $Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is$ (1) $\frac{1}{2} \frac{G m}{R}$ (2) $\frac{4 G m}{R}$ (3) $\frac{1}{2 R} \frac{1}{G m}$ (4) $.$ 308. $At some location on earth the horizontal component of earth's magnetic field is 18 \times 10^{- 6} T . At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45^{\circ} angle with horizontal in equilibrium. To keepthis needle horizontal, the vertical force that should beapplied at one of its ends is:$ (1) $3.6 \times 10^{- 5} N$ (2) $1.8 \times 10^{- 5} N$ (3) $1.3 \times 10^{- 5} N$ (4) $6.5 \times 10^{- 5} N$ 309. $A satellite is orbiting just above the surface of the earth with period T . If d is the density of the earth and G is the universal constant of gravitation, the quantity \frac{3 π}{G d} represents$ (1) $T^{2}$ (2) $T^{3}$ (3) $T$ (4) $T$ 310. $At what height from the surface of earth the gravitational potential and the value of g are - 5.4 \times 1 0^{7} J k g^{- 1} and 6.0 m s^{- 2} respectively? Take the radius of earth as 6400 km$ (1) $2000 km$ (2) $2600 km$ (3) $1600 km$ (4) $1400 km$ 311. $Given below are two statements: one is labelled as Assertion (a)and the other is labelled as Reason (R). Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant. Reason (R): For a central force field the angular momentum is a constant. In the light of the above statements, choose the most appropriate answer from the options given below:$ (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) $(A) is correct but (R) is not correct$ 312. $At what height from the surface of earth the gravitational potential and the value of g are - 5.4 \times 1 0^{7} J k g^{- 1} and 6.0 m s^{- 2} respectively? Take, the radius of earth as 6400 km. [NEET 2016]$ (1) $1600 km$ (2) $1400 km$ (3) $2000 km$ (4) $2600 km$ 313. $Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and plane i.e. T^{2} = K r^{3} here K is constant If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = \frac{GMm}{r ^{2}}, here G is gravitational constant The relation between G and K is described as:$ (1) $GMK = 4π2$ (2) $K = G$ (3) $K = \frac{1}{G}$ (4) $GK = 4π2$ 314. $Acceleration due to gravity.$ (1) $increases with altitude$ (2) $decreases with altitude$ (3) $is independent of altitude$ (4) $first decrease and then increases with altitude$ 315. $A period of geostationary satellite is$ (1) $30 h$ (2) $24 h$ (3) $48 h$ (4) $12 h$ 316. $Given below are two statements: Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. Statement II: The time period of revolution of the satellite is T = 2 π \frac{R _{e}}{g} (for satellite very close to the earth surface), where R_{e} radius of earth and g acceleration due to gravity. In the light of the above statements, choose the correct answer from the options given below:$ (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) $Both Statement I and Statement II are false$ 317. $Every planet revolves around the sun in an elliptical orbit: (A) The force acting on a planet is inversely proportional to square of distance from sun. (B) Force acting on planet is inversely proportional to product of the masses of the planet and the sun (C) The centripetal force acting on the planet is directed away from the sun. (D) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below:$ (1) $A and D only$ (2) $C and D only$ (3) $B and C only$ (4) $A and C only$ 318. $Choose the correct statement.$ (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) $Acceleration due to gravity decreases with increasing depth assuming earth to be a sphere of uniform density.$ 319. $Find the acceleration of our galaxy, due to the nearest comparably sized galaxy. The approximate masses of each galaxy is 8 \times 10^{11} solar mass and they are separated by 2 million light-years. Each galaxy has a diameter of 100000 light year. (Assume, 1 light year \approx 10^{16} m, gravitational constant, G \approx 10^{- 10} (\frac{Nm ^{2}}{kg ^{2}}) and mass of sun (= 2.0 \times 10^{30} kg)$ (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) $5 \times 10^{- 13} m / s^{2}$ 320. $A planet of mass M, has two natural satellites with masses m_{1} and m_{2} . The radii of their circular orbits are R_{1} and R_{2} respectively. Ignore the gravitational force between the satellites. Define v_{1}, L_{1}, K_{1} and T_{1} to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v_{2}, L_{2}, K_{2} and T_{2} to be the corresponding quantities of satellite 2. Given m_{1} / m_{2} = 2 and R_{1} / R_{2} = 1/4, match the ratios in List-I to the numbers in List-II. List-I P. \frac{v _{1}}{v _{2}} Q. \frac{L _{1}}{L _{2}} R. \frac{K _{1}}{K _{2}} S. \frac{T _{1}}{T _{2}} List-II 1. \frac{1}{8} 2. 1 3. 2 4. 8$ (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) $P \to 2; Q \to 3; R \to 4; S \to 1$ 321. $A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3 \times 1 0^{5} times heavier than the Earth and is at a distance 2.5 \times 1 0^{4} times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is v_{e} = 11.2km s^{-1} . The minimum initial velocity (v_{s}) required for the rocket to be able to leave the Sun-Earth system is closest to: (Ignore the rotation and revolution of the Earth and the presence of any other planet)$ (1) $v_{s} = 72 km s^{-1}$ (2) $v_{s} = 22 km s^{-1}$ (3) $v_{s} = 42 km s^{-1}$ (4) $v_{s} = 62 km s^{-1}$ 322. $Two particles of equal mass 'm' move in a circle of radius 'r' under the action of their mutual gravitational attraction. The speed of each particle will be:$ (1) $\frac{GM}{2 r}$ (2) $\frac{4 GM}{r}$ (3) $\frac{GM}{r}$ (4) $\frac{GM}{4 r}$ 323. $A body of weight W is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:$ (1) $\frac{W}{91}$ (2) $\frac{W}{100}$ (3) $\frac{W}{9}$ (4) $\frac{W}{3}$ 324. $The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be:$ (1) $3 years$ (2) $3 years$ (3) $9 years$ (4) $33 years$ 325. $The orbital period of a geostationary satellite is$ (1) $2 h$ (2) $5 h$ (3) $24 h$ (4) $12 h$ 326. $The escape velocity from earth is 11.2 km / s . If a body is to be projected in a direction making an angle 4 5^{o} to the vertical, then the escape velocity is$ (1) $11.2 \times 2 km / s$ (2) $11.2 km / s$ (3) $11.2/2 km / s$ (4) $11.22 km / s$ 327. $The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v . What will be its total energy?$ (1) $3/4 m v^{2}$ (2) $1/2 m v^{2}$ (3) $m v^{2}$ (4) $-1/2 m v^{2}$ 328. $Let ' g_{h}' and ' g_{d}' be the accelerations due to gravity at height ' h' above the earth's surface and at depth ' d' below the earth's surface respectively. If g_{h} = g_{d} then the relation between ' h' and ' d' is$ (1) $d = h$ (2) $d = \frac{h}{2}$ (3) $d = \frac{h}{4}$ (4) $d = 2 h$ 329. $If the earth suddenly shrinks to \frac{1}{64} th of its original volume with its mass remaining the same, the period of rotation of earth becomes \frac{24}{x} h . The value of x is$ 330. $If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth ah (h<< R_{e}) from the earth surface. The value of α will be_________.(use R_{e} =6400 km)$