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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.
| 2451. |
If the earth were to rotates faster than its present speed, the weight of an object will |
| A. | Increase at the equator but remain unchanged at the poles |
| B. | Decrease at the equator but remain unchanged at the poles |
| C. | Remain unchanged at the equator but decrease at the poles |
| D. | Remain unchanged at the equator but increase at the poles |
| Answer» C. Remain unchanged at the equator but decrease at the poles | |
| 2452. |
Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g?, then |
| A. | \[g'=g/9\] |
| B. | \[g'=27g\] |
| C. | \[g=9g\] |
| D. | \[g'=3g\] |
| Answer» E. | |
| 2453. |
The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be- |
| A. | 1/2 R |
| B. | 2 R |
| C. | 4 R |
| D. | ¼ R |
| Answer» B. 2 R | |
| 2454. |
A particle is suspended from a spring and it stretches the spring by 1 cm on the surface of earth. By how much amount the same particle will stretch the same spring at a place 800 km above the surface of earth. |
| A. | 1.59 cm |
| B. | 2.38 cm |
| C. | 0.79 cm |
| D. | 1.38 cm |
| Answer» D. 1.38 cm | |
| 2455. |
The height of the point vertically above the earth's surface, at which acceleration due to gravity becomes 1 % of its value at the earth's surface is (Radius of the earth = R) |
| A. | 8 R |
| B. | 9 R |
| C. | 10 R |
| D. | 20 R |
| Answer» C. 10 R | |
| 2456. |
The speed of earth's rotation about its axis is cd. Its speed is increases to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is: |
| A. | 1 |
| B. | 8.5 |
| C. | 17 |
| D. | 34 |
| Answer» D. 34 | |
| 2457. |
Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If \[{{\operatorname{R}}_{e}}\]is the maximum range of a projectile on the earth's surface, what is the maximum range on the surface of the moon for the same velocity of projection |
| A. | \[0.2{{\operatorname{R}}_{e}}\] |
| B. | \[2{{\operatorname{R}}_{e}}\] |
| C. | \[0.5{{\operatorname{R}}_{e}}\] |
| D. | \[5{{\operatorname{R}}_{e}}\] |
| Answer» E. | |
| 2458. |
Three particles P, Q and R are placed as per given figure. Masses of P, Q and R are \[\sqrt{3}m,\,\,\sqrt{3}m\] and m respectively. The gravitational force on a fourth particle S of mass m is equal to |
| A. | \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in ST direction only |
| B. | \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SQ direction and \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SU direction |
| C. | \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\] in SQ direction only |
| D. | \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SQ direction and \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\] in ST direction |
| Answer» D. \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SQ direction and \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\] in ST direction | |
| 2459. |
A central particle M is surrounded by a square array of other particles, separated by either distance d or distance d/2 along the perimeter of the square. The magnitude of the gravitational force on the central particle due to the other particles is |
| A. | \[\frac{9GMm}{{{d}^{2}}}\] |
| B. | \[\frac{5GMm}{{{d}^{2}}}\] |
| C. | \[\frac{3GMm}{{{d}^{2}}}\] |
| D. | \[\frac{GMm}{{{d}^{2}}}\] |
| Answer» D. \[\frac{GMm}{{{d}^{2}}}\] | |
| 2460. |
Two bodies of masses 4 kg and 9 kg are separated by a distance of 60 cm. A 1 kg mass is placed in between these two masses. If the net force on 1 kg is zero, then its distance from 4 kg mass is |
| A. | 26 cm |
| B. | 30 cm |
| C. | 28 cm |
| D. | 24 cm |
| Answer» E. | |
| 2461. |
If masses of two point objects is doubled and distance between them is tripled, then gravitational force of attraction between them will nearly |
| A. | Increase by 225% |
| B. | decrease by 44% |
| C. | Decrease by 56% |
| D. | increase by 125% |
| Answer» D. increase by 125% | |
| 2462. |
Two stars of mass \[{{\operatorname{m}}_{1}} and {{m}_{2}}\]are parts of a binary system. The radii of their orbits are \[{{r}_{1}} and {{r}_{2}}\]respectively, measured from the C.M. of the system. The magnitude of gravitational force \[{{\operatorname{m}}_{1}}\]exerts on \[{{m}_{2}}\]is |
| A. | \[\frac{{{m}_{1}}{{m}_{2}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] |
| B. | \[\frac{{{m}_{1}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] |
| C. | \[\frac{{{m}_{2}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] |
| D. | \[\frac{\left( {{m}_{1}}+{{m}_{2}} \right)}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] |
| Answer» B. \[\frac{{{m}_{1}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] | |
| 2463. |
A mass M is split into two parts m and (M- w), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts? |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{5}\] |
| Answer» C. \[\frac{1}{4}\] | |
| 2464. |
Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be |
| A. | \[\frac{F}{9}\] |
| B. | 3F |
| C. | F |
| D. | \[\frac{F}{3}\] |
| Answer» D. \[\frac{F}{3}\] | |
| 2465. |
The time taken by the earth to travel over half its orbit, remote from the sun, separated by the minor axis is about 2 days more than half the year, then the eccentricity of the orbit is |
| A. | 10959 |
| B. | 1/60 |
| C. | 42005 |
| D. | 25569 |
| Answer» C. 42005 | |
| 2466. |
For a particle inside a uniform spherical shell, the gravitational force on the particle is |
| A. | Infinite |
| B. | zero |
| C. | \[\frac{-G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] |
| D. | \[\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] |
| Answer» C. \[\frac{-G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] | |
| 2467. |
A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth's centre. Their time periods are in the ratio of |
| A. | 0.0430555555555556 |
| B. | 0.0527777777777778 |
| C. | 0.0638888888888889 |
| D. | \[1:2\sqrt{2}\] |
| Answer» E. | |
| 2468. |
In a gravitational field, at a point where the gravitational potential is zero |
| A. | the gravitational field is necessarily zero |
| B. | the gravitational field is not necessarily zero |
| C. | any value between one and infinite |
| D. | None of these |
| Answer» B. the gravitational field is not necessarily zero | |
| 2469. |
The distance of Neptune and Saturn from the sun is nearly \[1{{0}^{13}} and 1{{0}^{12}}\] meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio |
| A. | 10 |
| B. | 100 |
| C. | \[10\sqrt{10}\] |
| D. | 1000 |
| Answer» D. 1000 | |
| 2470. |
If the earth is at one-fourth of its present distance from the sun, the duration of the year will be |
| A. | half the present year |
| B. | one-eighth the present year |
| C. | one-sixth the present year |
| D. | one-tenth the present year |
| Answer» C. one-sixth the present year | |
| 2471. |
If the distance of earth is halved from the sun, then the no. of days in a year will be |
| A. | 365 |
| B. | 182.5 |
| C. | 730 |
| D. | 129 |
| Answer» E. | |
| 2472. |
The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If \[{{t}_{1}}\] is the time for the planet to move from C to D and \[{{t}_{2}}\] is the time to move from A to B then |
| A. | \[{{t}_{i}}=4{{t}_{2}}\] |
| B. | \[{{t}_{i}}=2{{t}_{2}}\] |
| C. | \[{{t}_{i}}={{t}_{2}}\] |
| D. | \[{{t}_{i}}>{{t}_{2}}\] |
| Answer» C. \[{{t}_{i}}={{t}_{2}}\] | |
| 2473. |
A straight rod of length L extends from \[x=a\]to\[x=L+a\]. Find the gravitational force it exerts on a point mass m at x = 0 if the linear density of rod\[\mu =A+B{{x}^{2}}\]. |
| A. | \[Gm\left[ \frac{A}{a}+BL \right]\] |
| B. | \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]\] |
| C. | \[Gm\left[ BL+\frac{A}{a+L} \right]\] |
| D. | \[Gm\left[ BL+\frac{A}{a} \right]\] |
| Answer» C. \[Gm\left[ BL+\frac{A}{a+L} \right]\] | |
| 2474. |
Two concentric uniform shells of mass \[{{M}_{1}}\] and \[{{M}_{2}}\] are as shown in the figure. A particle of mass m is located just within the shell \[{{M}_{2}}\] on its inner surface. Gravitational force on 'm' due to \[{{M}_{1}}\] and \[{{M}_{2}}\] will be |
| A. | Zero |
| B. | \[\frac{G{{M}_{1}}m}{{{b}^{2}}}\] |
| C. | \[\frac{G\left( {{M}_{1}}+{{M}_{2}} \right)m}{{{b}^{2}}}\] |
| D. | None of these |
| Answer» C. \[\frac{G\left( {{M}_{1}}+{{M}_{2}} \right)m}{{{b}^{2}}}\] | |
| 2475. |
Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is |
| A. | \[\sqrt{\frac{Gm}{4R}}\] |
| B. | \[\sqrt{\frac{Gm}{3R}}\] |
| C. | \[\sqrt{\frac{Gm}{2R}}\] |
| D. | \[\sqrt{\frac{Gm}{R}}\] |
| Answer» B. \[\sqrt{\frac{Gm}{3R}}\] | |
| 2476. |
If suddenly the gravitational force of attraction between Earth and a body revolving around it becomes zero, then the body will |
| A. | Continue to move in its orbit with same velocity |
| B. | Move tangentially to the original orbit with same velocity |
| C. | Become stationary in its orbit |
| D. | Move towards the earth |
| Answer» C. Become stationary in its orbit | |
| 2477. |
If three equal masses m are placed at the three vertices of an equilateral triangle of side \lm then what force acts on a particle of mass 2m placed at the centroid? |
| A. | \[G{{m}^{2}}\] |
| B. | \[2G{{m}^{2}}\] |
| C. | Zero |
| D. | \[-G{{m}^{2}}\] |
| Answer» D. \[-G{{m}^{2}}\] | |
| 2478. |
A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\] as shown in the figure. The gravitational field due to the ring at a distance \[\sqrt{3}r\]is. |
| A. | \[\frac{Gm}{8{{r}^{2}}}\] |
| B. | \[\frac{Gm}{4{{r}^{2}}}\] |
| C. | \[\sqrt{3}\frac{Gm}{8{{r}^{2}}}\] |
| D. | \[\frac{Gm}{8{{r}^{2}}\sqrt{3}}\] |
| Answer» D. \[\frac{Gm}{8{{r}^{2}}\sqrt{3}}\] | |
| 2479. |
Let \[\omega \] be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole\[(d |
| A. | \[\frac{{{\omega }^{2}}{{R}^{2}}}{g}\] |
| B. | \[\frac{{{\omega }^{2}}{{R}^{2}}}{2g}\] |
| C. | \[\frac{2{{\omega }^{2}}{{R}^{2}}}{g}\] |
| D. | \[\frac{\sqrt{Rg}}{g}\] |
| Answer» B. \[\frac{{{\omega }^{2}}{{R}^{2}}}{2g}\] | |
| 2480. |
In a Van de Graff generator, a spherical metal shell is to be \[15\times {{10}^{6}}V\] electrode. The dielectric strength of the gas surrounding the electrode is \[15\times {{10}^{-7}}V{{m}^{-1}}.\] The minimum radius of the spherical shell required is |
| A. | 1m |
| B. | 2m |
| C. | 1.5m |
| D. | 3m |
| Answer» E. | |
| 2481. |
For the configuration of media permittivities \[{{\varepsilon }_{0}},\varepsilon \] and \[{{\varepsilon }_{0}}\]between parallel plated each of area A, as shown in Fig. the equivalent capacitance |
| A. | \[{{\varepsilon }_{0}}A/d\] |
| B. | \[\varepsilon {{\varepsilon }_{0}}A/d\] |
| C. | \[\frac{\varepsilon {{\varepsilon }_{0}}A}{d\left( \varepsilon +{{\varepsilon }_{0}} \right)}\] |
| D. | \[\frac{\varepsilon {{\varepsilon }_{0}}A}{\left( 2\varepsilon +{{\varepsilon }_{0}} \right)d}\] |
| Answer» E. | |
| 2482. |
A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab. |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 2483. |
A parallel plate capacitor of area ?A? plate separation ?d? is filled with two dielectrics as shown. What is the capacitance of the arrangement? |
| A. | \[\frac{3K{{\varepsilon }_{0}}A}{4d}\] |
| B. | \[\frac{4K{{\varepsilon }_{0}}A}{4d}\] |
| C. | \[\frac{\left( K+1 \right){{\varepsilon }_{0}}A}{2d}\] |
| D. | \[\frac{K\left( K+3 \right){{\varepsilon }_{0}}A}{2\left( K+1 \right)d}\] |
| Answer» E. | |
| 2484. |
A capacitor of capacity \[{{C}_{1}}\] is charged up to V volt and then connected to an uncharged capacitor of capacity \[{{C}_{2}}.\] Then final potential difference across each will be |
| A. | \[\frac{{{C}_{2}}V}{{{C}_{1}}+{{C}_{2}}}\] |
| B. | \[\left( 1+\frac{{{C}_{2}}}{{{C}_{1}}} \right)V\] |
| C. | \[\frac{{{C}_{1}}V}{{{C}_{1}}+{{C}_{2}}}\,\] |
| D. | \[\,\left( 1-\frac{{{C}_{2}}}{{{C}_{1}}} \right)V\] |
| Answer» D. \[\,\left( 1-\frac{{{C}_{2}}}{{{C}_{1}}} \right)V\] | |
| 2485. |
An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential \[{{V}_{0}}.\] The two share the charge, and the common potential becomes V. The dielectric constant K is |
| A. | \[\frac{{{V}_{0}}}{V}-1\] |
| B. | \[\frac{{{V}_{0}}}{V}+1\] |
| C. | \[\frac{V}{{{V}_{0}}}-1\] |
| D. | \[\frac{V}{{{V}_{0}}}+1\] |
| Answer» B. \[\frac{{{V}_{0}}}{V}+1\] | |
| 2486. |
In figure, there is a four way key at the middle. If key is shown from situation BD to AD, then how much charge will flow through point O? |
| A. | \[24\mu C\] |
| B. | \[36\mu C\] |
| C. | \[72\mu C\] |
| D. | \[12\mu C\] |
| Answer» D. \[12\mu C\] | |
| 2487. |
Two parallel plate capacitors of capacitance C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected, and the region between the plates of C is filled completely with a material of dielectric constant K. The common potential difference across the combination becomes |
| A. | \[\frac{2V}{K+2}\] |
| B. | \[\frac{V}{K+2}\] |
| C. | \[\frac{3V}{K+3}\] |
| D. | \[\frac{3V}{K+2}\] |
| Answer» E. | |
| 2488. |
A parallel plate capacitor is located horizontally such that one of the plates is submerged in a liquid while the other is above the liquid surface. When plates are charged the level of liquid |
| A. | rises |
| B. | falls |
| C. | remains unchanged |
| D. | may rise or fall depending on the of charge amount |
| Answer» B. falls | |
| 2489. |
Four identical square plates of side a are arranged as shown. The equivalent capacity between A and C |
| A. | \[\frac{3{{\varepsilon }_{0}}{{a}^{2}}}{2d}\] |
| B. | \[\frac{3{{\varepsilon }_{0}}{{a}^{2}}}{5d}\] |
| C. | \[\frac{3{{\varepsilon }_{0}}{{a}^{2}}}{3d}\] |
| D. | \[\frac{5{{\varepsilon }_{0}}{{a}^{2}}}{3d}\] |
| Answer» D. \[\frac{5{{\varepsilon }_{0}}{{a}^{2}}}{3d}\] | |
| 2490. |
Two capacitors of capacitances and are connected in series, assume that the equivalent capacitance of this arrangement is C, where |
| A. | \[C<{{C}_{1}}/2\] |
| B. | \[{{C}_{1}}/2<C<{{C}_{2}}/2\] |
| C. | \[{{C}_{1}}<C<{{C}_{2}}\] |
| D. | \[{{C}_{2}}<C<2{{C}_{2}}\] |
| Answer» C. \[{{C}_{1}}<C<{{C}_{2}}\] | |
| 2491. |
A network of six identical capacitors, each of value C is made as shown in the figure. Equivalent capacitance between points A and B is |
| A. | C/4 |
| B. | 3C/4 |
| C. | 4C/3 |
| D. | 3C |
| Answer» D. 3C | |
| 2492. |
The capacitance of a metallic sphere is \[1\mu F\], then it?s radius is nearly |
| A. | 1.11 m |
| B. | 10 m |
| C. | 9 km |
| D. | 1.11 cm |
| Answer» D. 1.11 cm | |
| 2493. |
Capacitance (in F) of a spherical conductor with radius 1 m is |
| A. | \[1.1\times {{10}^{-10}}\] |
| B. | \[{{10}^{6}}\] |
| C. | \[9\times {{10}^{-9}}\] |
| D. | \[{{10}^{-3}}\] |
| Answer» B. \[{{10}^{6}}\] | |
| 2494. |
In the circuit given below, the charge in \[\mu C\] , on the capacitor having capacitance \[5\mu F\]is |
| A. | 4.5 |
| B. | 9 |
| C. | 7 |
| D. | 15 |
| Answer» C. 7 | |
| 2495. |
Three capacitors are connected in the arms of a triangle ABC as shown in figure 5 V is applied between A and B. The voltage between B and C is. |
| A. | 2 V |
| B. | 1 V |
| C. | 3 V |
| D. | 1.5 V |
| Answer» B. 1 V | |
| 2496. |
To obtain \[3\mu F\]capacity from three capacitors of \[2\mu F\]each, they will be arranged. |
| A. | all the three in series |
| B. | all the three in parallel |
| C. | two capacitors in series and the third in parallel with the combination of first two |
| D. | two capacitors in parallel and the third in series with the combination of first two |
| Answer» D. two capacitors in parallel and the third in series with the combination of first two | |
| 2497. |
Consider the situation shown in the figure. The capacitor A has a charge q on it whereas vB is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is |
| A. | zero |
| B. | \[q/2\] |
| C. | \[q\] |
| D. | \[2q\] |
| Answer» B. \[q/2\] | |
| 2498. |
The effective capacitance of combination of equal capacitors between points A and B shown in figure is. |
| A. | \[C\] |
| B. | \[2C\] |
| C. | \[3C\] |
| D. | \[\frac{C}{2}\] |
| Answer» C. \[3C\] | |
| 2499. |
A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance \[{{C}_{0}}\]. Now one-third of the material is replaced by another material with dielectric constant 2K, so that effectively there are two capacitors one with area \[\frac{1}{3}\]A, dialectic constant 2K and another with area \[\frac{2}{3}A\] and dielectric constant K. If the capacitance of this new capacitor is C then \[\frac{C}{{{C}_{0}}}\]is |
| A. | 1 |
| B. | \[\frac{4}{3}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{3}\] |
| Answer» C. \[\frac{2}{3}\] | |
| 2500. |
A parallel plate air capacitor has a capacitance of \[100\mu F.\]The plates are at a distance d apart. If a slab of thickness t(t |
| A. | \[50\mu F\] |
| B. | \[100\mu F\] |
| C. | \[200\mu F\] |
| D. | \[500\mu F\] |
| Answer» D. \[500\mu F\] | |