STD 11 - Gravitation PYQs: JEE Mains Physics

Showing 1–50 of 179 questions

1. 1. A body of mass \(m\) is taken from the surface of earth to a height equal to twice the radius of earth (\(R_e\)). The increase in potential energy will be _______.
   (\(g\) is acceleration due to gravity at the surface of earth) 2026 Medium
2. 2. A planet \((P_1)\) is moving around the star of mass \(2M\) in the orbit of radius \(R\). Another planet \((P_2)\) is moving around another star of mass \(4M\) in a orbit of radius \(2R\). Ratio of time periods of revolution of \(P_2\) and \(P_1\) is _______. 2026 Medium
3. 3. 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 \( T=2\pi\sqrt{\frac{R_{e}}{g}} \) (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 : 2026 Hard
4. 4. If a body of mass \(1\) kg falls on the earth from infinity, it attains velocity \((v)\) and kinetic energy \((k)\) on reaching the surface of earth. The values of \(v\) and \(k\) respectively are _______. (Take radius of earth to be \(6400\) km and \(g = 9.8\) m/s\(^2\)) 2026 Medium
5. 5. Initially a satellite of 100 kg is in a circular orbit of radius \(1.5 R _{ E }\). This satellite can be moved to a circular orbit of radius \(3 R _{ E }\) by supplying \(\alpha \times 10^6 J\) of energy. The value of \(\alpha\) is _________ .
   (Take Radius of Earth \(R_E=6 \times 10^6 m\) and \(g =10 m / s ^2\) ) 2026 Hard
6. 6. Net gravitational force at the centre of a square is found to be \( F_{1} \) when four particles having mass M, 2M, 3M and 4M are placed at the four corners of the square as shown in figure and it is \( F_{2} \) when the positions of 3M and 4M are interchanged. The ratio \( \frac{F_{1}}{F_{2}} \) is \( \frac{\alpha}{\sqrt{5}} \). The value of \( \alpha \) is __________ .
   2026 Easy
7. 7. The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is __________ m/s. 2026 Medium
8. 8. The height in terms of radius of the earth \((R)\), at which the acceleration due to gravity becomes \(\dfrac{g}{9}\), where \(g\) is acceleration due to gravity on earth's surface, is ______. 2026 Medium
9. 9. Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m . They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J. 2026 Easy
10. 10. When one moves from a point \(16\) km below the earth's surface to a point \(16\) km above the earth's surface. The change in \(g\) is approximately \(\alpha\) %. The value of \(\alpha\) is _____.
    (Take radius of the earth \(= 6400\) km.) 2026 Medium
11. 11. A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by 2025 Medium
12. 12. A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______ \( \times 10^{10}\text{ J} \).
    (Mass of earth \( = 6 \times 10^{24}\text{ kg} \), Radius of earth \( = 6.4 \times 10^6\text{ m} \), Gravitational constant \( = 6.67 \times 10^{-11}\text{ N m}^2\text{ kg}^{-2} \))
    2025 Medium
13. 13. A satellite of mass \(\frac{M}{2}\) is revolving around earth in a circular orbit at a height of \(\frac{R}{3}\) from earth surface. The angular momentum of the satellite is \(M \sqrt{\frac{G M R}{x}}\). The value of \(x\) is ______ , where \(M\) and \(R\) are the mass and radius of earth, respectively. ( G is the gravitational constant) 2025 Hard
14. 14. A small point of mass \(m\) is placed at a distance \(2 R\) from the centre ' \(O^{\prime}\) of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is \(\mathrm{F}_1\). A spherical part of radius \(\mathrm{R} / 3\) is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be \(\mathrm{F}_2\). The value of ratio \(\mathrm{F}_1: \mathrm{F}_2\) is _______.
    
    2025 Hard
15. 15. Acceleration due to gravity on the surface of earth is ' \(g\) '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \(\ldots\ldots\) g. 2025 Easy
16. 16. An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
    (Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant) 2025 Easy
17. 17. Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is \(11.2 \mathrm{~km} / \mathrm{s}\), the escape velocity in \(\mathrm{km} / \mathrm{s}\) from the planet will be : 2025 Easy
18. 18. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
    Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
    In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Easy
19. 19. Given below are two statements: one is labelled as Assertion \(\mathrm{A}\) and the other is labelled as Reason \(\mathrm{R}\) Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is \(\frac{1}{2} \mathrm{mgR}\), where R is the radius of earth.
    Reason \(\mathrm{R}\) : 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 option given below 2025 Easy
20. 20. 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 : 2025 Easy
21. 21. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
    Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
    In the light of the above statements, choose the correct answer from the options given below : 2025 Easy
22. 22. If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon \(=27\) days and gravitational attraction between the satellite and the moon is neglected. 2025 Medium
23. 23. Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time \(\mathrm{T}=4\) seconds. If the sides of the triangle are increased to length 2 a and also the masses of the spheres are made 2 m , then they will collide after _____ seconds. 2025 Medium
24. 24. Two planets, \(A\) and \(B\) are orbiting a common star in circular orbits of radius \(R_A\) and \(R_B\), respectively, with \(R_B=2 R_A\). The planet \(B\) is \(4 \sqrt{2}\) times more massive than planet \(A\). The ratio \(\left(\frac{L_B}{L_A}\right)\) of angular momentum \(\left(L_B\right)\) of planet \(B\) to that of planet \(A\left(L_A\right)\) is closest to integer ________. 2025 Medium
25. 25. A \(90 \mathrm{~kg}\) body placed at \(2 \mathrm{R}\) distance from surface of earth experiences gravitational pull of _______. ( \(\mathrm{R}=\) Radius of earth, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) ) 2024 Hard
26. 26. A light planet is revolving around a massive star in a circular orbit of radius \(R\) with a period of revolution \(T\). If the force of attraction between planet and star is proportional to \(\mathrm{R}^{-3 / 2}\) then choose the correct option. 2024 Hard
27. 27. 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 _______. 2024 Hard
28. 28. A planet takes \(200\) days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution? 2024 Hard
29. 29. A satellite of \(10^3 \mathrm{~kg}\) mass is revolving in circular orbit of radius \(2 \mathrm{R}\). If \(\frac{10^4 \mathrm{R}}{6} \mathrm{~J}\) energy is supplied to the satellite, it would revolve in a new circular orbit of radius _______.
    (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{R}=\) radius of earth) 2024 Hard
30. 30. A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) ) 2024 Hard
31. 31. A simple pendulum doing small oscillations at a place \(\mathrm{R}\) height above earth surface has time period of \(T_1=4 \mathrm{~s}\). \(T_2\) would be it's time period if it is brought to a point which is at a height \(2 R\) from earth surface. Choose the correct relation. \([R=\) radius of Earth]: 2024 Hard
32. 32. An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5 \mathrm{~km}\). From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}\). The value of \(x\) is _______. (take \(R_{\mathrm{e}}=6370 \mathrm{~km}\) ) 2024 Hard
33. 33. Assuming the earth to be a sphere of uniform mass density, a body weighed \(300 \mathrm{~N}\) on the surface of earth. How much it would weigh at \(R / 4\) depth under surface of earth? 2024 Hard
34. 34. At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as \(R\).) 2024 Hard
35. 35. Correct formula for height of a satellite from earths surface is _______. 2024 Hard
36. 36. Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______. 2024 Hard
37. 37. Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______. 2024 Hard
38. 38. Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). \(Assertion\) \((A)\) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun. \(Reason\) \((R)\): The moon takes less time to move around the earth than the time taken by the earth to move around the sun. In the light of the above statements, choose the most appropriate answer from the options given below: 2024 Hard
39. 39. Match list-\(I\) with list-\(II\):

    List-\(I\)	List-\(II\)
    \((A)\)Kinetic energy of plant	\((I)\) \(-\frac{\mathrm{GMm}}{\mathrm{a}}\)
    \((B)\) Gravaitatioin potentiyal energy of sun -plant system	\((II)\) \(\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
    \((C)\)Total mecaniacal energy of palnt	\((III)\) \(\frac{\mathrm{Gm}}{\mathrm{r}}\)
    \((D)\)Escap energyat the surface of plant for unit mass object	\((IV)\) \(-\frac{\mathrm{GMm}}{2 \mathrm{a}}\)

    (Where \(\mathrm{a}=\) radius of planet orbit, \(\mathrm{r}=\) radius of planet, \(M=\) mass of Sun, \(m=\) mass of planet)
    Choose the correct answer from the options given below: 2024 Hard
40. 40. The acceleration due to gravity on the surface of earth is \(g\). If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be : 2024 Hard
41. 41. The gravitational potential at a point above the surface of earth is \(-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}\) and the acceleration due to gravity at that point is \(6.4 \mathrm{~m} / \mathrm{s}^2\). Assume that the mean radius of earth to be \(6400 \mathrm{~km}\). The height of this point above the earth's surface is _______. 2024 Hard
42. 42. The mass of the moon is \(1 / 144\) times the mass of a planet and its diameter \(1 / 16\) times the diameter of a planet. If the escape velocity on the planet is \(\mathrm{v}\), the escape velocity on the moon will be _______. 2024 Hard
43. 43. To project a body of mass \(m\) from earth's surface to infinity, the required kinetic energy is _______. (assume, the radius of earth is \(R_E, g=\) acceleration due to gravity on the surface of earth) 2024 Hard
44. 44. Two planets \(A\) and \(B\) having masses \(m_1\) and \(m_2\) move around the sun in circular orbits of \(r_1\) and \(r_2\) radii respectively. If angular momentum of \(\mathrm{A}\) is \(\mathrm{L}\) and that of \(B\) is \(3L\), the ratio of time period \(\left(\frac{T_A}{T_B}\right)\) is _______. 2024 Hard
45. 45. Two satellite \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(\mathrm{A}\) is \(3 v\), the speed of \(\mathrm{B}\) will be _______. 2024 Hard
46. 46. A body is released from a height equal to the radius ( \(R\) ) of the earth. The velocity of the body when it strikes the surface of the earth will be : (Given \(g\) = acceleration due to gravity on the earth.) 2023 Medium
47. 47. A planet having mass \(9\,Me\) and radius \(4 R _e\), where Me and \(\operatorname{Re}\) are mass and radius of earth respectively, has escape velocity in \(km / s\) given by:(Given escape velocity on earth \(\left.V_e=11.2 \times 10^3\,m / s \right)\) 2023 Medium
48. 48. A spaceship of mass \(2 \times 10^4\,kg\) is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be \(......\) (if \(g =10\,m / s ^2\) and radius of earth \(=6400\,km\) ) 2023 Medium
49. 49. An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be : 2023 Medium
50. 50. Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its werght on the surface of earth is \(200\,N\), will be \(...........\,N\) ( \(Given R =\) Radrus of earth) 2023 Medium

No questions on this page match these filters. Clear filters