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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.
| 2401. |
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: |
| A. | 2600 km |
| B. | 1600 km |
| C. | 1400 km |
| D. | 2000 km |
| Answer» B. 1600 km | |
| 2402. |
Two bodies of masses \[{{M}_{1}}\text{ }\operatorname{and}\text{ }{{M}_{2}}\]are placed at a distanced/apart. What is the potential at the position where the gravitational field due to them is zero? |
| A. | \[-\frac{G}{d}({{M}_{1}}+{{M}_{2}}+2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] |
| B. | \[-\frac{G}{d}({{M}_{1}}+{{M}_{2}}-2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] |
| C. | \[-\frac{G}{d}(2{{M}_{1}}+{{M}_{2}}+2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] |
| D. | \[-\frac{G}{2d}({{M}_{1}}+{{M}_{2}}+2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] |
| Answer» B. \[-\frac{G}{d}({{M}_{1}}+{{M}_{2}}-2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] | |
| 2403. |
The period of moon's rotation around the earth is nearly 29 days. If moon's mass were 2 fold its present value and all other things remain unchanged, the period of moon's rotation would be nearly |
| A. | \[29\sqrt{2} days\] |
| B. | \[29/\sqrt{2} days\] |
| C. | \[29\times 2 days\] |
| D. | 29 days |
| Answer» E. | |
| 2404. |
The mass M of a planet-earth is uniformly distributed over a spherical volume of radius R. Calculate the energy needed to disassemble the planet against the gravitational pull amongst its constituent particles. Given: \[\operatorname{MR}=2.5\times 1{{0}^{31}} kg-mandg= 10m/{{s}^{2}}\] |
| A. | \[3.0\times {{10}^{32}}\operatorname{J}\] |
| B. | \[2.5\times {{10}^{32}}\operatorname{J}\] |
| C. | \[0.5\times {{10}^{32}}\operatorname{J}\] |
| D. | \[1.5\times {{10}^{32}}\operatorname{J}\] |
| Answer» E. | |
| 2405. |
A geo-stationary satellite orbits around the earth in a circular orbit of radius 36,000 km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface \[({{R}_{earth}} = 6,400km)\]will approximately be |
| A. | 1/2hr |
| B. | 1hr |
| C. | 2hr |
| D. | 4hr |
| Answer» D. 4hr | |
| 2406. |
Three equal masses (each m) are placed at the comers of an equilateral triangle of side 'a? Then the escape velocity of an object from the circumcentre P of triangle is: |
| A. | \[\sqrt{\frac{2\sqrt{3}Gm}{a}}\] |
| B. | \[\sqrt{\frac{\sqrt{3}Gm}{a}}\] |
| C. | \[\sqrt{\frac{6\sqrt{3}Gm}{a}}\] |
| D. | \[\sqrt{\frac{3\sqrt{3}Gm}{a}}\] |
| Answer» D. \[\sqrt{\frac{3\sqrt{3}Gm}{a}}\] | |
| 2407. |
The acceleration due to gravity on the surface of the moon is 1/6 that on the surface of earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities on earth and moon will be |
| A. | \[\frac{\sqrt{6}}{2}\] |
| B. | \[\sqrt{24}\] |
| C. | 3 |
| D. | \[\frac{\sqrt{3}}{2}\] |
| Answer» C. 3 | |
| 2408. |
A shell is fired vertically from the earth with speed \[\frac{{{V}_{esc}}}{N},\] where Nis some number greater than one and V is escape speed for the earth. Neglecting the nation of the earth and air resistance, the maximum altitude attained by the shell will be is radius of the earth) |
| A. | \[\frac{{{N}^{2}}{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\] |
| B. | \[\frac{N{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\] |
| C. | \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\] |
| D. | \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}}\] |
| Answer» D. \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}}\] | |
| 2409. |
In older times, people used to think that the earth was flat. Imagine that the earth is indeed not a sphere of radius R, but an infinite plate of thickness H. What value of is needed to allow the same gravitational acceleration to be experienced as on the surface of the actual earth? (Assume that the earth's density is uniform and equal in the two models |
| A. | 2R/3 |
| B. | 4R/3 |
| C. | 8R/3 |
| D. | R/3 |
| Answer» B. 4R/3 | |
| 2410. |
An asteroid of mass m is approaching earth initially at a distance of\[10{{\operatorname{R}}_{e}}\], with speed\[{{v}_{i}}\]. It hits the earth with a speed \[{{v}_{f}}({{\operatorname{R}}_{e}}\,\,and\,\,{{M}_{e}}\], are radius and mass of earth), then |
| A. | \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{M}_{e}}R}\left( 1-\frac{1}{10} \right)\] |
| B. | \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1+\frac{1}{10} \right)\] |
| C. | \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\] |
| D. | \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\] |
| Answer» D. \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\] | |
| 2411. |
A satellite of mass m is orbiting the earth in a circular orbit of radius R. It starts losing energy due to small air resistance at the rate of C J/s. Find the time taken for the satellite to reach the earth. |
| A. | \[\frac{GMm}{C}\left[ \frac{1}{R}-\frac{1}{r} \right]\] |
| B. | \[\frac{GMm}{2C}\left[ \frac{1}{R}+\frac{1}{r} \right]\] |
| C. | \[\frac{GMm}{2C}\left[ \frac{1}{R}-\frac{1}{r} \right]\] |
| D. | \[\frac{2GMm}{C}\left[ \frac{1}{R}+\frac{1}{r} \right]\] |
| Answer» D. \[\frac{2GMm}{C}\left[ \frac{1}{R}+\frac{1}{r} \right]\] | |
| 2412. |
Two spheres each of mass M are situated at a distance 2d (see figure). A particle of mass \[m(m |
| A. | \[\frac{7GMm}{d}\] |
| B. | \[\frac{8GMm}{d}\] |
| C. | \[-\frac{8GMm}{d}\] |
| D. | zero |
| Answer» E. | |
| 2413. |
In planetary motion the areal velocity of position vector of a planet depends on angular velocity\[(\omega )\] and the distance of the planet from sun (r). If so, the correct relation for areal velocity is |
| A. | \[\frac{dA}{dt}\propto \omega r\] |
| B. | \[\frac{dA}{dt}\propto {{\omega }^{2}}r\] |
| C. | \[\frac{dA}{dt}\propto \omega {{r}^{2}}\] |
| D. | \[\frac{dA}{dt}\propto \sqrt{\omega r}\] |
| Answer» D. \[\frac{dA}{dt}\propto \sqrt{\omega r}\] | |
| 2414. |
The radius of the earth is reduced by 4%. The mass of the earth remains unchanged. What will be the change in escape velocity? |
| A. | Increased by 2% |
| B. | Decreased by 4% |
| C. | Increased by 6% |
| D. | Decreased by 8% |
| Answer» B. Decreased by 4% | |
| 2415. |
For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required? |
| A. | 0.41 |
| B. | 0.61 |
| C. | 0.81 |
| D. | 0.98 |
| Answer» B. 0.61 | |
| 2416. |
A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is |
| A. | \[\frac{g{{R}^{2}}}{R+x}\] |
| B. | \[\frac{g{{R}^{2}}}{R-x}\] |
| C. | \[gx\] |
| D. | \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\] |
| Answer» E. | |
| 2417. |
An artificial satellite is first taken to a height equal to half the radius of earth. Assume that it is at rest on the earth's surface initially and that it is at rest at this height. Let \[{{E}_{1}}\]be the energy required. It is then given the appropriate orbital speed such that it goes in a circular orbit at that height. Let E be the energy required. The ratio \[\frac{{{E}_{1}}}{{{E}_{2}}}\] is |
| A. | 0.167361111111111 |
| B. | 3:1 |
| C. | 0.0423611111111111 |
| D. | 0.0430555555555556 |
| Answer» D. 0.0430555555555556 | |
| 2418. |
With what minimum speed should m be projected from point C in presence of two fixed masses M each at A and B as shown in the figure such that mass m should escape the gravitational attraction of A and B |
| A. | \[\sqrt{\frac{2GM}{R}}\] |
| B. | \[\sqrt{\frac{2\sqrt{2}GM}{R}}\] |
| C. | \[2\sqrt{\frac{GM}{R}}\] |
| D. | \[2\sqrt{2}\sqrt{\frac{GM}{R}}\] |
| Answer» C. \[2\sqrt{\frac{GM}{R}}\] | |
| 2419. |
A sky lab of mass m kg is first launched from the surface of the earth in a circular orbit of radius 2R (from the centre of the earth) and then it is shifted form this circular orbit of radius 3R. The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are |
| A. | \[\frac{3}{4}\operatorname{mgR}, \frac{mgR}{6}\] |
| B. | \[\frac{3}{4}\operatorname{mgR}, \frac{mgR}{12}\] |
| C. | \[\operatorname{mgR}, mgR\] |
| D. | \[2\operatorname{mgR}, mgR\] |
| Answer» C. \[\operatorname{mgR}, mgR\] | |
| 2420. |
A space vehicle approaching a planet has a speed v, when it is very far from the planet. At that moment tangent of its trajectory would miss the centre of the planet by distance R. If the planet has mass M and radius r, what is the smallest value of R in order that the resulting orbit of the space vehicle will just miss the surface of the planet? |
| A. | \[\frac{r}{v}{{\left[ {{v}^{2}}+\frac{2GM}{r} \right]}^{\frac{1}{2}}}\] |
| B. | \[\operatorname{vr}\left[ 1+\frac{2GM}{r} \right]\] |
| C. | \[\frac{r}{v}\left[ {{v}^{2}}+\frac{2GM}{r} \right]\] |
| D. | \[\frac{2GMv}{r}\] |
| Answer» B. \[\operatorname{vr}\left[ 1+\frac{2GM}{r} \right]\] | |
| 2421. |
The gravitational field, due to the 'left over part* of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly): |
| A. | \[\frac{5}{6}\frac{GM}{{{x}^{2}}}\] |
| B. | \[\frac{8}{9}\frac{GM}{{{x}^{2}}}\] |
| C. | \[\frac{7}{8}\frac{GM}{{{x}^{2}}}\] |
| D. | \[\frac{6}{7}\frac{GM}{{{x}^{2}}}\] |
| Answer» D. \[\frac{6}{7}\frac{GM}{{{x}^{2}}}\] | |
| 2422. |
A point P lies on the axis of a fixed ring of mass M and radius R, at a distance 2R from its centre O. A small particle starts from P and reaches O under gravitational attraction only. Its speed at O will be |
| A. | Zero |
| B. | \[\sqrt{\frac{2Gm}{R}}\] |
| C. | \[\sqrt{\frac{2Gm}{R}\left( \sqrt{5}-1 \right)}\] |
| D. | \[\sqrt{\frac{2Gm}{R}\left( 1-\frac{1}{\sqrt{5}} \right)}\] |
| Answer» E. | |
| 2423. |
A planet revolves about the sun in elliptical orbit. The areal velocity \[\left( \frac{dA}{dt} \right)\] of the planet is\[4.0\times 1{{0}^{16}} m/s\]. The least distance between planet and the sun is\[2\times {{10}^{12}}m\]. Then the maximum speed of the planet in km/s is |
| A. | 10 |
| B. | 20 |
| C. | 30 |
| D. | 40 |
| Answer» E. | |
| 2424. |
In a certain region of space, gravitational field is given by\[I=-(K/r)\]. Taking the reference point to be at \[r={{r}_{0}}\]with \[V={{V}_{0}},\] find the potential. |
| A. | \[K\,\log \frac{r}{{{r}_{0}}}+{{V}_{0}}\] |
| B. | \[K\,\log \frac{{{r}_{0}}}{r}+{{V}_{0}}\] |
| C. | \[K\,\log \frac{r}{{{r}_{0}}}-{{V}_{0}}\] |
| D. | \[\log \frac{{{r}_{0}}}{r}-{{V}_{0}}r\] |
| Answer» B. \[K\,\log \frac{{{r}_{0}}}{r}+{{V}_{0}}\] | |
| 2425. |
Gravitational field at the centre of a semicircle formed by a thin wire AB of mass m and length \[\ell \]is |
| A. | \[\frac{Gm}{{{\ell }^{2}}}\operatorname{along}+x-axis\] |
| B. | \[\frac{Gm}{\pi {{\ell }^{2}}}\operatorname{along}+y-axis\] |
| C. | \[\frac{2\pi Gm}{{{\ell }^{2}}}\operatorname{along}+x-axis\] |
| D. | \[\frac{2\pi Gm}{{{\ell }^{2}}}\operatorname{along}+y-axis\] |
| Answer» E. | |
| 2426. |
Inside a uniform sphere of density p there is a spherical cavity whose centre is at a distance \[\ell \]from the centre of the sphere. Find the strength F of the gravitational field inside the cavity at the point P. |
| A. | \[\frac{4}{3}G\pi \rho \vec{\ell }\] |
| B. | \[\frac{1}{3}G\pi \rho \vec{\ell }\] |
| C. | \[\frac{2}{3}G\pi \rho \vec{\ell }\] |
| D. | \[\frac{1}{2}G\pi \rho \vec{\ell }\] |
| Answer» B. \[\frac{1}{3}G\pi \rho \vec{\ell }\] | |
| 2427. |
Three identical stars, each of mass M, form an equilateral triangle (stars are positioned at the comers) that rotates around the centre of-the triangle. The system is isolated and edge length of the triangle is L. The amount of work done, that is required to dismantle the system is: |
| A. | (a)\[\frac{3G{{M}^{2}}}{L}\] |
| B. | \[\frac{3G{{M}^{2}}}{2L}\] |
| C. | \[\frac{3G{{M}^{2}}}{4L}\] |
| D. | \[\frac{G{{M}^{2}}}{2L}\] |
| Answer» C. \[\frac{3G{{M}^{2}}}{4L}\] | |
| 2428. |
The gravitational potential at the centre of a square of side 'a? and four equal masses (m each) placed at the comers of a square is |
| A. | Zero |
| B. | \[4\sqrt{2}\frac{Gm}{a}\] |
| C. | \[-4\sqrt{2}\frac{Gm}{a}\] |
| D. | \[-4\sqrt{2}\frac{G{{m}^{2}}}{a}\] |
| Answer» D. \[-4\sqrt{2}\frac{G{{m}^{2}}}{a}\] | |
| 2429. |
A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre |
| A. | Increases |
| B. | decreases |
| C. | remains constant |
| D. | cannot say |
| Answer» B. decreases | |
| 2430. |
Let V and E denote the gravitational potential and gravitational field at a point. It is possible to have |
| A. | (a)\[V=O\text{ }and\text{ }E=0\] |
| B. | \[\operatorname{V}=0 and E\ne 0\] |
| C. | \[\operatorname{V}\ne 0 and E=0\] |
| D. | All of the above |
| Answer» E. | |
| 2431. |
Radius of moon is 1/4 times that of earth and mass is 1/81 times that of earth. The point at which gravitational field due to earth becomes equal and opposite to that of moon, is (Distance between centres of earth and moon is 60R, where R is radius of earth) |
| A. | 5.75 R from centre of moon |
| B. | 16 R from surface of moon |
| C. | 53 R from centre of earth |
| D. | 54 R from centre of earth |
| Answer» E. | |
| 2432. |
If ?g? is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass 'm' raised from the surface of the earth to a height equal to the radius 'R' of the earth is |
| A. | \[\frac{1}{4}mgr\] |
| B. | \[\frac{1}{2}mgr\] |
| C. | \[2\,mgr\] |
| D. | \[mgr\] |
| Answer» C. \[2\,mgr\] | |
| 2433. |
The figure shows a planet in elliptical orbit around the sun 5'. Where is the kinetic energy of the planet maximum? |
| A. | \[{{P}_{1}}\] |
| B. | \[{{P}_{2}}\] |
| C. | \[{{P}_{3}}\] |
| D. | \[{{P}_{4}}\] |
| Answer» E. | |
| 2434. |
Intensity of the gravitational field inside the hollow spherical shell is |
| A. | Variable |
| B. | minimum |
| C. | Maximum |
| D. | zero |
| Answer» E. | |
| 2435. |
Two concentric spherical shells are as shown in figure. Choose the correct statement given below. |
| A. | Potential at A is greater than B |
| B. | Gravitational field at A is less than B |
| C. | As one moves from C to D then potential remains constant |
| D. | As one moves from D to A then gravitational field decreases |
| Answer» D. As one moves from D to A then gravitational field decreases | |
| 2436. |
Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then |
| A. | g decreases by 2% and K decreases by 4% |
| B. | g decreases by 4% and K increases by 2% |
| C. | g increases by 4% and K decreases by 4% |
| D. | g decreases by 4% and K increases by 4% |
| Answer» D. g decreases by 4% and K increases by 4% | |
| 2437. |
The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon\[=7.36\times 1{{0}^{22}} kg\], radius of the moon's orbit\[= 3.8\times 1{{0}^{8}} m\]). |
| A. | \[6.73\times 1{{0}^{-5}} m/{{s}^{2}}\] |
| B. | \[6.73\times 1{{0}^{-3}} m/{{s}^{2}}\] |
| C. | \[6.73\times 1{{0}^{-2}} m/{{s}^{2}}\] |
| D. | \[6.73\times 1{{0}^{-4}} m/{{s}^{2}}\] |
| Answer» B. \[6.73\times 1{{0}^{-3}} m/{{s}^{2}}\] | |
| 2438. |
The radii of two planets are respectively \[{{R}_{1}}\] and \[{{R}_{2}}\] their densities are respectively\[{{\rho }_{1}} and {{\rho }_{2}}\]. The ratio of the accelerations due to gravity at their surfaces is |
| A. | \[{{g}_{1}}:{{g}_{2}}=\frac{{{\rho }_{1}}}{{{R}_{1}}^{2}}:\frac{{{\rho }_{2}}}{{{R}_{2}}^{2}}\] |
| B. | \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{R}_{2}}:{{\rho }_{1}}{{\rho }_{2}}\] |
| C. | \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{R}_{2}}:{{R}_{2}}{{\rho }_{1}}\] |
| D. | \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{\rho }_{1}}:{{R}_{2}}{{\rho }_{2}}\] |
| Answer» E. | |
| 2439. |
The depth d at which the value of acceleration due to gravity becomes \[\frac{1}{n}\] times the value at the surface of the earth, is [R = radius of the earth] |
| A. | \[\frac{R}{n}\] |
| B. | \[R\left( \frac{n-1}{n} \right)\] |
| C. | \[\frac{R}{{{n}^{2}}}\] |
| D. | \[R\left( \frac{n}{n+1} \right)\] |
| Answer» C. \[\frac{R}{{{n}^{2}}}\] | |
| 2440. |
While approaching a planet circling a distant star, an astronaut determines the radius of a planet is half of that of the earth. After landing on its surface, he finds its acceleration due to gravity is twice as that of the earth. The ratio of the mass of planet and that of the earth. |
| A. | 0.0430555555555556 |
| B. | 0.0854166666666667 |
| C. | 0.127777777777778 |
| D. | 0.170138888888889 |
| Answer» B. 0.0854166666666667 | |
| 2441. |
If the radius of the earth were to shrink by 1 %, with its mass remaining the same, the acceleration due to gravity on the earth's surface would |
| A. | Decrease by 1% |
| B. | decrease by 2% |
| C. | Increase by 1% |
| D. | increase by 2% |
| Answer» E. | |
| 2442. |
Assuming the radius of the earth as R, the change in gravitational potential energy of a body of mass m, when it is taken from the earth's surface to a height 3R above its surface, is |
| A. | \[3\text{ }mgR\] |
| B. | \[\frac{3}{4}mgR\] |
| C. | \[\text{1 }mgR\] |
| D. | \[\frac{3}{2}mgR\] |
| Answer» C. \[\text{1 }mgR\] | |
| 2443. |
R is the radius of the earth and co is its angular velocity and \[{{\operatorname{g}}_{p}}\]is the value of g at the poles. The effective value of g at the latitude \[\lambda = 60{}^\circ \] will be equal to |
| A. | \[{{g}_{p}}-\frac{1}{4}R{{\omega }^{2}}\] |
| B. | \[{{g}_{p}}-\frac{3}{4}R{{\omega }^{2}}\] |
| C. | \[{{g}_{p}}-R{{\omega }^{2}}\] |
| D. | \[{{g}_{p}}+\frac{1}{4}R{{\omega }^{2}}\] |
| Answer» B. \[{{g}_{p}}-\frac{3}{4}R{{\omega }^{2}}\] | |
| 2444. |
The value of 'g' at a particular point is\[9.8 m/{{s}^{2}}\]. Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass. The value of 'g? at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will now be |
| A. | \[4.9\,\,m/se{{c}^{2}}\] |
| B. | \[3.1\,\,m/se{{c}^{2}}\] |
| C. | \[9.8\,\,m/se{{c}^{2}}\] |
| D. | \[19.6\,\,m/se{{c}^{2}}\] |
| Answer» D. \[19.6\,\,m/se{{c}^{2}}\] | |
| 2445. |
The ratio of radii of earth to another planet is 21 3 and the ratio of their mean densities is 4/5. If an astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is |
| A. | 1 m |
| B. | 0.8 m |
| C. | 0.5 m |
| D. | 125 m |
| Answer» C. 0.5 m | |
| 2446. |
The value of acceleration due to gravity on moving from equator to poles will |
| A. | Decrease |
| B. | increase |
| C. | Remain same |
| D. | become half |
| Answer» C. Remain same | |
| 2447. |
A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at \[\frac{a}{2}\] distance from the centre, will be: |
| A. | \[-\frac{3GM}{a}\] |
| B. | \[-\frac{2GM}{a}\] |
| C. | \[-\frac{GM}{a}\] |
| D. | \[-\frac{4GM}{a}\] |
| Answer» B. \[-\frac{2GM}{a}\] | |
| 2448. |
Two spherical bodies of mass M and 5M& radii R & 2R respectively 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 just before collision is |
| A. | 2.5 R |
| B. | 4.5 R |
| C. | 7.5 R |
| D. | 1.5 R |
| Answer» D. 1.5 R | |
| 2449. |
Consider two solid uniform spherical objects of the same density p. One has radius R and the other has radius 2R. They are in outer space where the gravitational field from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction? |
| A. | \[G{{\pi }^{2}}{{R}^{2}}\] |
| B. | \[\frac{128}{81}G{{\pi }^{2}}{{R}^{4}}{{\rho }^{2}}\] |
| C. | \[\frac{128}{81}G{{\pi }^{2}}\] |
| D. | \[\frac{128}{81}{{\pi }^{2}}{{R}^{4}}G\] |
| Answer» C. \[\frac{128}{81}G{{\pi }^{2}}\] | |
| 2450. |
Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Then, velocity of a particle is given by |
| A. | \[{{\left[ \frac{Gm}{r}\left( \frac{1+2\sqrt{2}}{4} \right) \right]}^{\frac{1}{2}}}\] |
| B. | \[\sqrt{\frac{Gm}{r}}\] |
| C. | \[\sqrt{\frac{Gm}{r}}\left( 1+2\sqrt{2} \right)\] |
| D. | \[a{{\left[ \frac{1}{2}\frac{Gm}{r}\left( \frac{1+2\sqrt{2}}{2} \right) \right]}^{\frac{1}{2}}}\] |
| Answer» B. \[\sqrt{\frac{Gm}{r}}\] | |