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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 6401. |
The escape velocity from earth is \[{{v}_{es}}.\] A body is projected with velocity \[2{{v}_{es}}\]with what constant velocity will it move in the inter planetary space [DCE 2002] |
| A. | \[{{v}_{es}}\] |
| B. | \[3{{v}_{es}}\] |
| C. | \[\sqrt{3}{{v}_{es}}\] |
| D. | \[\sqrt{5}{{v}_{es}}\] |
| Answer» D. \[\sqrt{5}{{v}_{es}}\] | |
| 6402. |
A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take \[G=6.67\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}})\] [AIEEE 2005] |
| A. | \[6.67\times {{10}^{9}}J\] |
| B. | \[6.67\times {{10}^{10}}J\] |
| C. | \[13.34\times {{10}^{10}}J\] |
| D. | \[3.33\times {{10}^{10}}J\] |
| Answer» C. \[13.34\times {{10}^{10}}J\] | |
| 6403. |
A planet has twice the radius but the mean density is \[\frac{1}{4}th\] as compared to earth. What is the ratio of escape velocity from earth to that from the planet [MH CET 2004] |
| A. | 3 : 1 |
| B. | 1 : 2 |
| C. | 1 : 1 |
| D. | 2 : 1 |
| Answer» D. 2 : 1 | |
| 6404. |
If the radius and acceleration due to gravity both are doubled, escape velocity of earth will become [RPMT 2002] |
| A. | 11.2 km/s |
| B. | 22.4 km/s |
| C. | 5.6 km/s |
| D. | 44.8 km/s |
| Answer» C. 5.6 km/s | |
| 6405. |
If the radius of a planet is four times that of earth and the value of g is same for both, the escape velocity on the planet will be [RPET 2002] |
| A. | \[11.2\,\,km/s\] |
| B. | \[5.6\,\,km/s\] |
| C. | \[22.4\,\,km/s\] |
| D. | None |
| Answer» D. None | |
| 6406. |
The masses and radii of the earth and moon are \[{{M}_{1}},\,{{R}_{1}}\] and \[{{M}_{2}},\,{{R}_{2}}\] respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is [MP PET 1997] |
| A. | \[2\sqrt{\frac{G}{d}({{M}_{1}}+{{M}_{2}})}\] |
| B. | \[2\sqrt{\frac{2G}{d}({{M}_{1}}+{{M}_{2}})}\] |
| C. | \[2\sqrt{\frac{Gm}{d}({{M}_{1}}+{{M}_{2}})}\] |
| D. | \[2\sqrt{\frac{Gm({{M}_{1}}+{{M}_{2}})}{d({{R}_{1}}+{{R}_{2}})}}\] |
| Answer» B. \[2\sqrt{\frac{2G}{d}({{M}_{1}}+{{M}_{2}})}\] | |
| 6407. |
The acceleration due to gravity on a planet is same as that on earth and its radius is four times that of earth. What will be the value of escape velocity on that planet if it is \[{{v}_{e}}\] on earth [RPET 2002] |
| A. | \[{{v}_{e}}\] |
| B. | \[2{{v}_{e}}\] |
| C. | \[4{{v}_{e}}\] |
| D. | \[\frac{{{v}_{e}}}{2}\] |
| Answer» C. \[4{{v}_{e}}\] | |
| 6408. |
The escape velocity for a body of mass 1 kg from the earth surface is \[11.2\,\,km{{s}^{-1}}.\] The escape velocity for a body of mass 100 kg would be [DCE 2003] |
| A. | \[11.2\times {{10}^{2}}\,km{{s}^{-1}}\] |
| B. | \[11.2\,\,km{{s}^{-1}}\] |
| C. | \[11.2\,\times {{10}^{-2}}\,km{{s}^{-1}}\] |
| D. | None of these |
| Answer» C. \[11.2\,\times {{10}^{-2}}\,km{{s}^{-1}}\] | |
| 6409. |
If V, R and g denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is [MP PMT 2004] |
| A. | \[V=\sqrt{gR}\] |
| B. | \[V=\sqrt{\frac{4}{3}g{{R}^{3}}}\] |
| C. | \[V=R\sqrt{g}\] |
| D. | \[V=\sqrt{2gR}\] |
| Answer» E. | |
| 6410. |
The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45o with the vertical, the escape velocity will be [AIEEE 2003] |
| A. | \[\frac{11}{\sqrt{2}}km/s\] |
| B. | \[11\sqrt{2}\,km/s\] |
| C. | 22 km/s |
| D. | 11 km/s |
| Answer» E. | |
| 6411. |
The escape velocity for the earth is \[{{v}_{e}}\]. The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is [MP PET 2003] |
| A. | \[36\,{{v}_{e}}\] |
| B. | \[12\,{{v}_{e}}\] |
| C. | \[6\,{{v}_{e}}\] |
| D. | \[20\,{{v}_{e}}\] |
| Answer» C. \[6\,{{v}_{e}}\] | |
| 6412. |
The radius of a planet is \[\frac{1}{4}\] of earth?s radius and its acceleration due to gravity is double that of earth?s acceleration due to gravity. How many times will the escape velocity at the planet?s surface be as compared to its value on earth?s surface [BCECE 2003; MH CET 2000] |
| A. | \[\frac{1}{\sqrt{2}}\] |
| B. | \[\sqrt{2}\] |
| C. | \[2\sqrt{2}\] |
| D. | 2 |
| Answer» B. \[\sqrt{2}\] | |
| 6413. |
The velocity with which a projectile must be fired so that it escapes earth?s gravitation does not depend on [AIIMS 2003] |
| A. | Mass of the earth |
| B. | Mass of the projectile |
| C. | Radius of the projectile?s orbit |
| D. | Gravitational constant |
| Answer» C. Radius of the projectile?s orbit | |
| 6414. |
Escape velocity on the surface of earth is \[11.2\,km/s\]. Escape velocity from a planet whose mass is the same as that of earth and radius 1/4 that of earth is [CBSE PMT 2000; JIPMER 2002; BHU 2004] |
| A. | 2.8 km/s |
| B. | 15.6 km/s |
| C. | 22.4 km/s |
| D. | 44.8 km/s |
| Answer» D. 44.8 km/s | |
| 6415. |
The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is \[({{v}_{e}}\] is the escape velocity of earth) [Kerala (Med.) 2002] |
| A. | \[\sqrt{2/3}\,{{v}_{e}}\] |
| B. | \[\sqrt{3/2}\,{{v}_{e}}\] |
| C. | \[\sqrt{2}/3\,{{v}_{e}}\] |
| D. | \[2/\sqrt{3}\,{{v}_{e}}\] |
| Answer» B. \[\sqrt{3/2}\,{{v}_{e}}\] | |
| 6416. |
A mass of \[6\times {{10}^{24}}kg\] is to be compressed in a sphere in such a way that the escape velocity from the sphere is \[3\times {{10}^{8}}m\,/s\]. Radius of the sphere should be \[(G=6.67\times {{10}^{-11}}N-{{m}^{2}}/k{{g}^{2}})\] [UPSEAT 2002] |
| A. | 9 km |
| B. | 9 m |
| C. | 9 cm |
| D. | 9 mm |
| Answer» E. | |
| 6417. |
The ratio of the radii of planets A and B is \[{{k}_{1}}\] and ratio of acceleration due to gravity on them is \[{{k}_{2}}\]. The ratio of escape velocities from them will be [BHU 2002] |
| A. | \[{{k}_{1}}{{k}_{2}}\] |
| B. | \[\sqrt{{{k}_{1}}{{k}_{2}}}\] |
| C. | \[\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\] |
| D. | \[\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}\] |
| Answer» C. \[\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\] | |
| 6418. |
The change in potential energy, when a body of mass m is raised to a height nR from the earth's surface is (R = Radius of earth) [MP PMT 1996] |
| A. | \[mgR\frac{n}{n-1}\] |
| B. | nmgR |
| C. | \[mgR\frac{{{n}^{2}}}{{{n}^{2}}+1}\] |
| D. | \[mgR\frac{n}{n+1}\] |
| Answer» E. | |
| 6419. |
The escape velocity of a rocket launched from the surface of the earth [UPSEAT 2001] |
| A. | Does not depend on the mass of the rocket |
| B. | Does not depend on the mass of the earth |
| C. | Depends on the mass of the planet towards which it is moving |
| D. | Depends on the mass of the rocket |
| Answer» B. Does not depend on the mass of the earth | |
| 6420. |
If acceleration due to gravity on the surface of a planet is two times that on surface of earth and its radius is double that of earth. Then escape velocity from the surface of that planet in comparison to earth will be [RPET 2001] |
| A. | \[2{{v}_{e}}_{{}}\] |
| B. | \[3{{v}_{e}}_{{}}\] |
| C. | \[4{{v}_{e}}_{{}}\] |
| D. | None of these |
| Answer» B. \[3{{v}_{e}}_{{}}\] | |
| 6421. |
Escape velocity on the earth [BHU 2001] |
| A. | Is less than that on the moon |
| B. | Depends upon the mass of the body |
| C. | Depends upon the direction of projection |
| D. | Depends upon the height from which it is projected |
| Answer» E. | |
| 6422. |
If the radius of a planet is R and its density is \[\rho \], the escape velocity from its surface will be [MP PMT 2001] |
| A. | \[{{v}_{e}}\propto \rho R\] |
| B. | \[{{v}_{e}}\propto \sqrt{\rho }R\] |
| C. | \[{{v}_{e}}\propto \frac{\sqrt{\rho }}{R}\] |
| D. | \[{{v}_{e}}\propto \frac{1}{\sqrt{\rho }R}\] |
| Answer» C. \[{{v}_{e}}\propto \frac{\sqrt{\rho }}{R}\] | |
| 6423. |
Escape velocity on earth is 11.2 km/s. What would be the escape velocity on a planet whose mass is 1000 times and radius is 10 times that of earth [DCE 2001; DPMT 2004] |
| A. | 112 km/s |
| B. | 11.2 km/s |
| C. | 1.12 km/s |
| D. | 3.7 km/s |
| Answer» B. 11.2 km/s | |
| 6424. |
How many times is escape velocity \[({{V}_{e}})\], of orbital velocity \[({{V}_{0}})\] for a satellite revolving near earth [RPMT 2000] |
| A. | \[\sqrt{2}\] times |
| B. | 2 times |
| C. | 3 times |
| D. | 4 times |
| Answer» B. 2 times | |
| 6425. |
The least velocity required to throw a body away from the surface of a planet so that it may not return is (radius of the planet is \[6.4\times {{10}^{6}}m,\,\,g=9.8\,m/se{{c}^{2}})\] [AMU (Engg.) 1999] |
| A. | \[9.8\times {{10}^{-3}}m/sec\] |
| B. | \[12.8\times {{10}^{3}}m/sec\] |
| C. | \[9.8\times {{10}^{3}}m/sec\] |
| D. | \[11.2\times {{10}^{3}}m/sec\] |
| Answer» E. | |
| 6426. |
The angular velocity of rotation of star (of mass M and radius R) at which the matter start to escape from its equator will be [MH CET 1999] |
| A. | \[\sqrt{\frac{2G{{M}^{2}}}{R}}\] |
| B. | \[\sqrt{\frac{2GM}{g}}\] |
| C. | \[\sqrt{\frac{2GM}{{{R}^{3}}}}\] |
| D. | \[\sqrt{\frac{2GR}{M}}\] |
| Answer» D. \[\sqrt{\frac{2GR}{M}}\] | |
| 6427. |
Given mass of the moon is 1/81 of the mass of the earth and corresponding radius is 1/4 of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is [CPMT 1997; AIIMS 2000; Pb. PMT 2001] |
| A. | 0.14 km/s |
| B. | 0.5 km/s |
| C. | 2.5 km/s |
| D. | 5 km/s |
| Answer» D. 5 km/s | |
| 6428. |
The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become [CBSE PMT 1997] |
| A. | 5.6 km/s |
| B. | 11.2 km/s (remain unchanged) |
| C. | 22.4 km/s |
| D. | 44.8 km/s |
| Answer» D. 44.8 km/s | |
| 6429. |
The mass of the earth is \[6.00\times {{10}^{24}}\,kg\] and that of the moon is \[7.40\times {{10}^{22}}\,kg\]. The constant of gravitation \[G=6.67\times {{10}^{-11}}\,N-{{m}^{2}}/k{{g}^{2}}\]. The potential energy of the system is \[-7.79\times {{10}^{28}}\,joules\]. The mean distance between the earth and moon is [MP PMT 1995] |
| A. | \[3.80\times {{10}^{8}}\,metres\] |
| B. | \[3.37\times {{10}^{6}}\,metres\] |
| C. | \[7.60\times {{10}^{4}}\,metres\] |
| D. | \[1.90\times {{10}^{2}}\,metres\] |
| Answer» B. \[3.37\times {{10}^{6}}\,metres\] | |
| 6430. |
The escape velocity on earth is 11.2 km/s. On another planet having twice radius and 8 times mass of the earth, the escape velocity will be [Bihar CMEET 1995] |
| A. | 3.7 km/s |
| B. | 11.2 km/s |
| C. | 22.4 km/s |
| D. | 43.2 km/s |
| Answer» D. 43.2 km/s | |
| 6431. |
The escape velocity of an object on a planet whose g value is 9 times on earth and whose radius is 4 times that of earth in km/s is [EAMCET 1994] |
| A. | 67.2 |
| B. | 33.6 |
| C. | 16.8 |
| D. | 25.2 |
| Answer» B. 33.6 | |
| 6432. |
The escape velocity of a planet having mass 6 times and radius 2 times as that of earth is [CPMT 1999; MP PET 2003; Pb. PET 2002] |
| A. | \[\sqrt{3}\,{{V}_{e}}\] |
| B. | \[3\,{{V}_{e}}\] |
| C. | \[\sqrt{2}\,{{V}_{e}}\] |
| D. | \[2\,{{V}_{e}}\] |
| Answer» B. \[3\,{{V}_{e}}\] | |
| 6433. |
The escape velocity for the earth is 11.2 km/sec. The mass of another planet is 100 times that of the earth and its radius is 4 times that of the earth. The escape velocity for this planet will be [MP PMT 1999; Pb. PMT 2002] |
| A. | 112.0 km/s |
| B. | 5.6 km/s |
| C. | 280.0 km/s |
| D. | 56.0 km/s |
| Answer» E. | |
| 6434. |
How much energy will be necessary for making a body of 500 kg escape from the earth \[[g=9.8\,m/{{s}^{2}}\], radius of earth \[=6.4\times {{10}^{6}}\,m]\] [MP PET 1999] |
| A. | About \[9.8\times {{10}^{6}}\,J\] |
| B. | About \[6.4\times {{10}^{8}}\,J\] |
| C. | About \[3.1\times {{10}^{10}}\,J\] |
| D. | About \[27.4\times {{10}^{12}}\,J\] |
| Answer» D. About \[27.4\times {{10}^{12}}\,J\] | |
| 6435. |
The mass of the earth is 81 times that of the moon and the radius of the earth is 3.5 times that of the moon. The ratio of the escape velocity on the surface of earth to that on the surface of moon will be [MP PMT/PET 1998; JIPMER 2000] |
| A. | 0.2 |
| B. | 2.57 |
| C. | 4.81 |
| D. | 0.39 |
| Answer» D. 0.39 | |
| 6436. |
Escape velocity on a planet is \[{{v}_{e}}\]. If radius of the planet remains same and mass becomes 4 times, the escape velocity becomes [MP PMT 1996; DPMT 1999] |
| A. | \[4\,{{v}_{e}}\] |
| B. | \[2\,{{v}_{e}}\] |
| C. | \[{{v}_{e}}\] |
| D. | \[\frac{1}{2}{{v}_{e}}\] |
| Answer» C. \[{{v}_{e}}\] | |
| 6437. |
The escape velocity of an object from the earth depends upon the mass of the earth (M), its mean density \[(\rho )\], its radius (R) and the gravitational constant (G). Thus the formula for escape velocity is [MP PMT 1995] |
| A. | \[v=R\sqrt{\frac{8\pi }{3}G\rho }\] |
| B. | \[v=M\sqrt{\frac{8\pi }{3}GR}\] |
| C. | \[v=\sqrt{2GMR}\] |
| D. | \[v=\sqrt{\frac{2GM}{{{R}^{2}}}}\] |
| Answer» B. \[v=M\sqrt{\frac{8\pi }{3}GR}\] | |
| 6438. |
For the moon to cease to remain the earth's satellite, its orbital velocity has to increase by a factor of [MP PET 1994] |
| A. | 2 |
| B. | \[\sqrt{2}\] |
| C. | \[1/\sqrt{2}\] |
| D. | \[\sqrt{3}\] |
| Answer» C. \[1/\sqrt{2}\] | |
| 6439. |
The gravitational field due to a mass distribution is \[E=K/{{x}^{3}}\] in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is [MP PET 1994] |
| A. | \[K/x\] |
| B. | \[K/2x\] |
| C. | \[K/{{x}^{2}}\] |
| D. | \[K/2{{x}^{2}}\] |
| Answer» E. | |
| 6440. |
The escape velocity of a particle of mass m varies as [CPMT 1978; RPMT 1999; AIEEE 2002] |
| A. | \[{{m}^{2}}\] |
| B. | m |
| C. | \[{{m}^{0}}\] |
| D. | \[{{m}^{-1}}\] |
| Answer» D. \[{{m}^{-1}}\] | |
| 6441. |
The escape velocity of a projectile from the earth is approximately [DPMT 1982, 84; RPMT 1997; BHU 1998] |
| A. | 11.2 m/sec |
| B. | 112 km/sec |
| C. | 11.2 km/sec |
| D. | 11200 km/sec |
| Answer» D. 11200 km/sec | |
| 6442. |
If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is [NCERT 1975; RPET 2003] |
| A. | gr |
| B. | \[\sqrt{2gr}\] |
| C. | \[g/r\] |
| D. | \[r/g\] |
| Answer» C. \[g/r\] | |
| 6443. |
The escape velocity from the earth is about 11 km/second. The escape velocity from a planet having twice the radius and the same mean density as the earth, is [NCERT 1980; MP PMT 1987; MP PET 2001, 2003; AIIMS 2001; UPSEAT 1999] |
| A. | 22 km/sec |
| B. | 11 km/sec |
| C. | 5.5 km/sec |
| D. | 15.5 km/sec |
| Answer» B. 11 km/sec | |
| 6444. |
The escape velocity for a rocket from earth is 11.2 km/sec. Its value on a planet where acceleration due to gravity is double that on the earth and diameter of the planet is twice that of earth will be in km/sec [NCERT 1983; CPMT 1990; MP PMT 2000; UPSEAT 1999] |
| A. | 11.2 |
| B. | 5.6 |
| C. | 22.4 |
| D. | 53.6 |
| Answer» D. 53.6 | |
| 6445. |
The escape velocity of a sphere of mass m from earth having mass M and radius R is given by [NCERT 1981, 84; CBSE PMT 1999] |
| A. | \[\sqrt{\frac{2GM}{R}}\] |
| B. | \[2\sqrt{\frac{GM}{R}}\] |
| C. | \[\sqrt{\frac{2GMm}{R}}\] |
| D. | \[\sqrt{\frac{GM}{R}}\] |
| Answer» B. \[2\sqrt{\frac{GM}{R}}\] | |
| 6446. |
\[{{v}_{e}}\] and \[{{v}_{p}}\] denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then [NCERT 1974; MP PMT 1994] |
| A. | \[{{v}_{e}}={{v}_{p}}\] |
| B. | \[{{v}_{e}}={{v}_{p}}/2\] |
| C. | \[{{v}_{e}}=2{{v}_{p}}\] |
| D. | \[{{v}_{e}}={{v}_{p}}/4\] |
| Answer» C. \[{{v}_{e}}=2{{v}_{p}}\] | |
| 6447. |
A particle falls towards earth from infinity. It?s velocity on reaching the earth would be [Orissa JEE 2003] |
| A. | Infinity |
| B. | \[\sqrt{2gR}\] |
| C. | \[2\sqrt{gR}\] |
| D. | Zero |
| Answer» C. \[2\sqrt{gR}\] | |
| 6448. |
In a gravitational field, at a point where the gravitational potential is zero [CPMT 1990] |
| A. | The gravitational field is necessarily zero |
| B. | The gravitational field is not necessarily zero |
| C. | Nothing can be said definitely about the gravitational field |
| D. | None of these |
| Answer» B. The gravitational field is not necessarily zero | |
| 6449. |
In some region, the gravitational field is zero. The gravitational potential in this region [BVP 2003] |
| A. | Must be variable |
| B. | Must be constant |
| C. | Cannot be zero |
| D. | Must be zero |
| Answer» C. Cannot be zero | |
| 6450. |
Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to [BHU 2003; CPMT 2004] |
| A. | \[\frac{1}{R}\] |
| B. | \[\frac{1}{\sqrt{R}}\] |
| C. | R |
| D. | \[\frac{1}{{{R}^{3/2}}}\] |
| Answer» B. \[\frac{1}{\sqrt{R}}\] | |