Gravitation · JEE Main previous year questions

2019 10 questions

1. Q532019 · 12 Apr 2019 · Shift 2

   The ratio of the weights of a body on the Earth's surface to that on the surface of a planets is $9:4$. The mass of the planet is $\frac{1}{9}$ th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)

   1. A.$\frac{R}{9}$
   2. B.$\frac{R}{2}$
   3. C.$\frac{R}{3}$
   4. D.$\frac{R}{4}$
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   Answer: B

2. Q522019 · 10 Apr 2019 · Shift 1

   The value of acceleration due to gravity at Earth's surface is $9.8\mathrm{m}{\mathrm{s}}^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9\mathrm{m}{\mathrm{s}}^{-2}$, is close to : (Radius of earth $=6.4\times 10^6\mathrm{m}$)

   1. A.$1.6\times 10^6\mathrm{m}$
   2. B.$9.0\times 10^6\mathrm{m}$
   3. C.$6.4\times 10^6\mathrm{m}$
   4. D.$2.6\times 10^6\mathrm{m}$
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   Answer: D

3. Q442019 · 10 Apr 2019 · Shift 2

   A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given ; Mass of planet $=8\times 10^{22}\mathrm{kg}$, Radius of planet $=2\times 10^6\mathrm{m}$, Gravitational constant $\mathrm{G}=6.67\times 10^{-11}\mathrm{N}{\mathrm{m}}^2/k{\mathrm{g}}^2$]

   1. A.13
   2. B.9
   3. C.17
   4. D.11
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   Answer: D

4. Q412019 · 9 Apr 2019 · Shift 1

   A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be :

   1. A.$\frac{GM}{3a^2}$
   2. B.$\frac{2GM}{9a^2}$
   3. C.$\frac{GM}{9a^2}$
   4. D.$\frac{2GM}{3a^2}$
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   Answer: A

5. Q492019 · 9 Apr 2019 · Shift 2

   A test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho (r)=\frac{K}{r^2}$. Identify the correct relation between the radius R of the particle's orbit and its period T

   1. A.${\mathrm{T}}^2/{\mathrm{R}}^3$ is a constant
   2. B.TR is a constant
   3. C.$T/{\mathrm{R}}^2$ is a constant
   4. D.T/R is a constant
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   Answer: D

6. Q472019 · 8 Apr 2019 · Shift 2

   The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to : [Boltzmann Constant $k_B=1.38\times 10^{-23}J/K$ Avogadro Number $N_A=6.02\times 10^{26}/kg$ Radius of Earth : $6.4\times 10^6\mathrm{m}$ Gravitational acceleration on Earth = $10\mathrm{m}{\mathrm{s}}^{-2}$]

   1. A.$3\times 10^5\mathrm{K}$
   2. B.$10^4\mathrm{K}$
   3. C.650 K
   4. D.800 K
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   Answer: B

7. Q462019 · 12 Jan 2019 · Shift 1

   A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :

   1. A.in the same circular orbit of radius R
   2. B.such that it escapes to infinity
   3. C.in a circular orbit of a different radius
   4. D.in an elliptical orbit
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   Answer: D

8. Q492019 · 12 Jan 2019 · Shift 1

   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. A.$Gm\left[A\left(\frac{1}{a}-\frac{1}{a+L}\right)-BL\right]$
   2. B.$Gm\left[A\left(\frac{1}{a}-\frac{1}{a+L}\right)+BL\right]$
   3. C.$Gm\left[A\left(\frac{1}{a+L}-\frac{1}{a}\right)+BL\right]$
   4. D.$Gm\left[A\left(\frac{1}{a+L}-\frac{1}{a}\right)-BL\right]$
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   Answer: B

9. Q342019 · 12 Jan 2019 · Shift 2

   Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, $T_A/T_B$, is ;

   1. A.2
   2. B.$\frac{1}{2}$
   3. C.$\sqrt{\frac{1}{2}}$
   4. D.1
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   Answer: D

10. Q442019 · 9 Jan 2019 · Shift 1

    A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m ($m\ll M$). When the car is at rest, the speed of transverse waves in the string is $60{\text{ ms}}^{-1}$. When the car has acceleration a, the wave-speed increases to $60.5{\text{ ms}}^{-1}$. The value of a, in terms of gravitational acceleration g, is closest to :

    1. A.$\frac{g}{30}$
    2. B.$\frac{g}{5}$
    3. C.$\frac{g}{10}$
    4. D.$\frac{g}{20}$
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    Answer: B