Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

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.

2201.

The radius of the coil of a tangent galvanometer is 16cm. How many turns of the wire should be used if a current of 40m A is to produced at deflection of \[45{}^\circ \]. given, horizontal component of earth's field is \[0.36\times {{10}^{-4}}T\].

A. 458
B. 229  
C. 200
D. 115
Answer» C. 200
2202.

A compass needle placed at a distance r from a short magnet in Tan A position shows a deflection of \[60{}^\circ \]. If the distance is increased to r \[{{(3)}^{1/3}}\], then deflection of compass needle is

A. \[{{30}^{o}}\]
B. \[60\times {{3}^{\frac{1}{3}}}\]
C. \[60\times {{3}^{\frac{2}{3}}}\]
D. \[60\times {{3}^{\frac{3}{3}}}\]
Answer» B. \[60\times {{3}^{\frac{1}{3}}}\]
2203.

A dip needle lies initially in the magnetic meridian when it shows an angle of dip \[\theta \] at a place. The dip circle is rotated through an angle x in the horizontal plane and then it shows an angle of dip\[\theta \]. Then \[\frac{\tan \,\theta '}{\tan \,\theta }\]is

A. \[\frac{1}{\cos \,x}\]
B. \[\frac{1}{\sin \,x}\]
C. \[\frac{1}{\tan \,x}\]
D. \[\cos \,x\]
Answer» B. \[\frac{1}{\sin \,x}\]
2204.

A compass needle whose magnetic moment is\[60\,A{{m}^{2}}\], is directed towards geographical north at any place experiencing moment of force of\[1.2\times {{10}^{-3}}Nm\]. At that place the horizontal component of earth field is 40 micro\[W/{{m}^{2}}\]. What is the value of dip angle at that place?

A. \[30{}^\circ \]
B. \[60{}^\circ \]  
C. \[45{}^\circ \]
D. \[15{}^\circ \]
Answer» B. \[60{}^\circ \]  
2205.

Time periods of vibation of two bar magnets in sum and difference positions are 4 sec and 6 sec respectively. The ratio of their magnetic moments \[{{M}_{1}}/{{M}_{2}}\]is          

A. 6 : 4 
B. 1.26111111111111
C. 2.6 : 1
D. 1.5 : 1
Answer» D. 1.5 : 1
2206.

A permanent magnet in the shape of a thin cylinder of length \[10\text{ }cm\] has magnetization \[(M)={{10}^{6}}\,A\,{{m}^{-1}}\]. Its magnetization current\[{{I}_{M}}\]is

A. \[{{10}^{5}}\,A\]
B. \[{{10}^{6}}\,A\]
C. \[{{10}^{7}}\,A\]
D. \[{{10}^{8}}\,A\]
Answer» B. \[{{10}^{6}}\,A\]
2207.

Two magnets of same size and mass make respectively 10 and 15 oscillations per minute at certain place. The ratio of their magnetic moments is

A. 0.172916666666667
B. 0.377777777777778
C. 0.0854166666666667
D. 0.126388888888889
Answer» B. 0.377777777777778
2208.

The earth?s magnetic field lines resemble that of a dipole at centre of the earth. If the magnetic moment of this dipole is close to\[8\times {{10}^{22}}A{{m}^{2}}\], the value of earth?s magnetic field near the equator is close to (radius of the earth \[=6.4\times {{10}^{6}}m\])

A. 0.6 Gauss
B. 1.2 Gauss
C. 1.8 Gauss
D. 0.32 Gauss
Answer» B. 1.2 Gauss
2209.

At a place, if the earth?s horizontal and vertical components of magnetic fields are equal, then the angle of dip will be

A. \[30{}^\circ \]  
B. \[90{}^\circ \]
C. \[45{}^\circ \]
D. \[0{}^\circ \]
Answer» D. \[0{}^\circ \]
2210.

One can define'..A'. of a place as the vertical plane which passes through the imaginary line joining the magnetic North and the south-poles. Here, A refers to

A. geographic meridian
B. magnetic meridian
C. magnetic declination
D. magnetic inclination
Answer» C. magnetic declination
2211.

The strength of the earth?s magnetic field is

A. constant everywhere       
B. zero everywhere
C. having very high value
D. vary from place to place on the earth?s surface
Answer» E.
2212.

If the angular momentum of an electron is \[\vec{J}\] then the magnitude of the magnetic moment will be

A. \[\frac{eJ}{m}\]
B. \[\frac{eJ}{2m}\]
C. \[eJ\,2m\]          
D. \[\frac{2m}{eJ}\]          
Answer» C. \[eJ\,2m\]          
2213.

Two identical short bar magnets, each having magnetic moment of \[10\,A{{m}^{2}}\], are arranged such that their axial lines are perpendicular to each other and their centres be along the same straight line in a horizontal plane. If the distance between their centres is 0.2 m, the resultant magnetic induction at a point midway between them is \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}\,H{{m}^{-1}})\]

A. \[\sqrt{2}\times {{10}^{-7}}\,tesla\]
B. \[\sqrt{5}\times {{10}^{-7}}\,tesla\]
C. \[\sqrt{2}\times {{10}^{-3}}\,tesla\]
D. \[\sqrt{5}\times {{10}^{-3}}\,tesla\]
Answer» E.
2214.

A bar magnet has a length 8 cm. The magnetic field at a point at a distance 3 cm from the centre in the broad side-on position is found to be\[4\times {{10}^{-6}}T\]. The pole strength of the magnet is.

A. \[6\times {{10}^{-5}}Am\]
B. \[5\times {{10}^{-5}}Am\]
C. \[2\times {{10}^{-4}}Am\]
D. \[3\times {{10}^{-4}}Am\]
Answer» B. \[5\times {{10}^{-5}}Am\]
2215.

A bar magnet having a magnetic moment of \[2\times {{10}^{4}}J{{T}^{-1}}\] is free to rotate in a horizontal plane. A horizontal magnetic field \[B=6\times {{10}^{-4}}T\] exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction \[60{}^\circ \] from the field is

A. 12 J     
B. 6 J
C. 2 J       
D. 0.6 J
Answer» C. 2 J       
2216.

A magnet of magnetic moment M is rotated through \[{{360}^{o}}\] in a magnetic field H, the work done will be

A. \[MH\]  
B. \[2MH\]
C. \[2\pi MH\]        
D. Zero
Answer» E.
2217.

A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15A. If it is equivalent to a magnet of the same size and magnetization \[\vec{M}\] (magnetic moment/volume), then \[\left| \left. {\vec{M}} \right| \right.\] is:

A. \[30000\pi \,A{{m}^{-1}}\]      
B. \[3\pi \,A{{m}^{-1}}\]
C. \[30000\,A{{m}^{-1}}\]           
D. \[300\,A{{m}^{-1}}\]
Answer» D. \[300\,A{{m}^{-1}}\]
2218.

A magnetic dipole is acted upon by two magnetic Fields which are inclined to each other at an angle of \[{{75}^{o}}\]. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of \[{{30}^{o}}\]with this field. The magnitude of the other field (in mT) is close to:

A. 1
B. 11
C. 36
D. 1060
Answer» C. 36
2219.

A circular coil of 16 turns and radius 10cm carries a current of 0.75 A and rest with its plane normal to an external magnetic field of \[5.0\times {{10}^{-2}}T\]. The coil is free to rotate about its stable equilibrium position with a frequency of \[2.0\,{{s}^{-1}}\] Compute the moment of inertia of the coil about its axis of rotation.                 

A. \[3.4\times {{10}^{-5}}\,kg\,{{m}^{2}}\] 
B. \[1.2\times {{10}^{-4}}\,kg\,{{m}^{2}}\]
C. \[2.6\times {{10}^{-4}}\,kg\,{{m}^{2}}\]  
D.        \[4.7\times {{10}^{-5}}\,kg\,{{m}^{2}}\]
Answer» C. \[2.6\times {{10}^{-4}}\,kg\,{{m}^{2}}\]  
2220.

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is \[60{}^\circ \] and one of the fields has a magnitude of \[1.2\times {{10}^{-2}}T\]. If the dipole comes to stable equilibrium at an angle of \[15{}^\circ \] with this field, what is the magnitude of other field?

A. \[4.4\times {{10}^{-3}}\,tesla\]
B. \[5.2\times {{10}^{-3}}\,tesla\]
C. \[3.4\times {{10}^{-3}}\,tesla\]
D. \[7.8\times {{10}^{-3}}\,tesla\]
Answer» B. \[5.2\times {{10}^{-3}}\,tesla\]
2221.

Two short bar magnets P and Q are arranged such that their centres are on the X-axis and are separated by a large distance. The magnetic axes of P and Q are along X and Y axes respectively. At a point R, midway between their centres, if B is the magnitude of induction due to Q, the magnitude of total induction at R due to the both magnets is

A. 3B
B. \[\sqrt{5}B\]
C. \[\frac{\sqrt{5}}{2}B\]
D. \[B\]
Answer» C. \[\frac{\sqrt{5}}{2}B\]
2222.

A bar magnet of length \['\ell '\] and magnetic dipole moment ?M? is bent in the form of an are as shown in figure. The new magnetic dipole moment will be 

A. \[\frac{3}{\pi }M\]
B. \[\frac{2}{\pi }M\]
C. \[\frac{M}{2}\]
D. M
Answer» B. \[\frac{2}{\pi }M\]
2223.

The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance x, (x>>d). The force between them is proportional to \[{{x}^{-n}}\] where n is:

A. 1
B. 2     
C. 3
D. 4
Answer» E.
2224.

A bar magnet having centre 0 has a length of 4 cm. Point \[{{P}_{1}}\]is in the broad side-on and \[{{P}_{2}}\] is in the end side-on position with \[O{{P}_{1}}=O{{P}_{2}}=10\] metres. The ratio of magnetic intensities H at \[{{P}_{1}}\] and \[{{P}_{2}}\]is

A. \[{{H}_{1}}:{{H}_{2}}=16:100\]
B. \[{{H}_{1}}:{{H}_{2}}=1:2\]
C. \[{{H}_{1}}:{{H}_{2}}=2:1\]
D. \[{{H}_{1}}:{{H}_{2}}=100:16\]
Answer» C. \[{{H}_{1}}:{{H}_{2}}=2:1\]
2225.

A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through\[60{}^\circ \]. The torque required to maintain the needle in this position will be

A. \[\sqrt{3}W\]
B. W    
C. \[\frac{\sqrt{3}}{2}W\]
D.  2W
Answer» B. W    
2226.

Force between two identical bar magnets whose centres are r metre apart is 4.8 N, when their axes are in the same line. If separation is increased to r, the force between them is

A. 2.4 N
B. 1.2N
C. 0.6 N
D. 0.3 N
Answer» E.
2227.

Two identical magnetic dipoles of magnetic moments\[1.0\,A\,-{{m}^{2}}\], each, placed at a separation of 2m with their axis perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is

A. \[5\times {{10}^{-7}}\,T\]
B. \[\sqrt{5}\times {{10}^{-7}}\,T\]
C. \[{{10}^{-7}}\,T\]
D. None of these
Answer» C. \[{{10}^{-7}}\,T\]
2228.

The net magnetic moment of two identical magnets each of magnetic moment \[{{M}_{0}}\], inclined at \[60{}^\circ \] with each other is

A. \[{{M}_{0}}\]  
B. \[\sqrt{2}\,{{M}_{0}}\]
C. \[\sqrt{3}\,{{M}_{0}}\] 
D. \[2{{M}_{0}}\]
Answer» D. \[2{{M}_{0}}\]
2229.

If a bar magnet of pole strength m and magnetic moment M is cut perpendicular to its axis in two equal halves then its new pole strength m' and magnetic moment M' are respectively

A. \[m'=m\] and \[M'=M\]
B. \[m'=m\] and \[M'=\frac{M}{2}\]
C. \[m'=\frac{m}{2}\] and \[M'=2M\]
D. \[m'=2m\] and \[M'=\frac{M}{2}\]
Answer» C. \[m'=\frac{m}{2}\] and \[M'=2M\]
2230.

A car is negotiating a curved road of radius R. The road is banked at an angle\[\theta \]. The coefficient of friction between the tyres of the car and the road is\[{{\mu }_{s}}\]. The maximum safe velocity on this road is:

A. \[\sqrt{g{{R}^{2}}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\]
B. \[\sqrt{gR\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\]
C. \[\sqrt{\frac{g}{R}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\]
D. \[\sqrt{\frac{g}{{{R}^{2}}}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\]
Answer» C. \[\sqrt{\frac{g}{R}\frac{{{\mu }_{s}}+\tan \theta }{1-{{\mu }_{s}}\tan \theta }}\]
2231.

A conical pendulum of length 1 m makes an angle \[\theta =45{}^\circ \] w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below 0. The speed of the pendulum, in its circular path, will be:   (Take \[g=10m{{s}^{-2}}\])

A. 0.4 m/s
B. 4 m/s
C. 0.2 m/s
D. 2 m/s
Answer» E.
2232.

In the given figure, a smooth parabolic wire track lies in the xy-plane (vertical). The shape of track is defined by the equation\[y={{x}^{2}}\]. A ring of mass m which can slide freely on the wire track, is placed at the position A (1,1). The track is rotated with constant angular speed to such there is no relative slipping between the ring and the track. The value of \[\omega \] is        

A. \[\sqrt{g/2}\]
B. \[\sqrt{g}\]
C. \[\sqrt{2g}\]
D. \[2\sqrt{g}\]
Answer» E.
2233.

An aircraft executes a horizontal loop with a speed of 150 m/s with its wings banked at an angle of \[12{}^\circ .\] The radius of the loop is : \[\left( g=10m/{{s}^{2}} \right)\]

A. 10.6 km
B. 9.6 km
C. 7.4 km
D. 5.8 km
Answer» B. 9.6 km
2234.

A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity \[\sqrt{3gr}\] at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

A. \[4:3\]
B. \[5:4\]  
C. \[1:4\]
D. \[3:2\]
Answer» D. \[3:2\]
2235.

A bridge is in the form of a semi-circle of radius 40m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is \[\left( g=10\text{ }m{{s}^{-2}} \right)\] (frictional force is negligibly small)

A. \[40\text{ }m{{s}^{-1}}\]
B. \[20\text{ }m{{s}^{-1}}\]
C. \[30\text{ }m{{s}^{-1}}\]
D. \[\text{15 }m{{s}^{-1}}\]
Answer» C. \[30\text{ }m{{s}^{-1}}\]
2236.

A particle of mass m rotates with a uniform angular speed\[\omega \]. It is viewed from a frame rotating about the z-axis with a uniform angular velocity\[{{\omega }_{0}}\]. The centrifugal force on the particle is:

A. \[m{{\omega }^{2}}r\]
B. \[m{{\omega }^{2}}r\]
C. \[m\left( \frac{\omega +{{\omega }_{0}}}{2} \right)a\]
D. zero
Answer» C. \[m\left( \frac{\omega +{{\omega }_{0}}}{2} \right)a\]
2237.

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is

A. \[0{}^\circ \]  
B. \[\frac{\pi }{3}\]
C. \[\frac{\pi }{6}\]  
D. \[\frac{\pi }{4}\]
Answer» E.
2238.

A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down is

A. \[\sqrt{gR}\]
B. \[\sqrt{2gR}\]
C. \[\sqrt{3gR}\]
D. \[\sqrt{5gR}\]
Answer» B. \[\sqrt{2gR}\]
2239.

Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration \[3\text{ }m/{{s}^{2}}\]in east direction. When person A stops pulling, it moves with acceleration \[1\text{ }m/{{s}^{2}}\]in the west direction. When person B stops pulling, it moves with acceleration \[\text{24 }m/{{s}^{2}}\] in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their directions same as the old directions, is

A. \[\text{24 }m/{{s}^{2}}\]
B. \[\text{3}\sqrt{71}\text{ }m/{{s}^{2}}\]
C. \[\text{30 }m/{{s}^{2}}\]
D. \[\text{25 }m/{{s}^{2}}\]
Answer» E.
2240.

An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is\[\mu \text{ }=\text{ }1\]. Assume that it can move in any direction, up the incline or down the incline then

A. The maximum possible acceleration of the insect can be \[14\text{ }m/{{s}^{2}}\]
B. The maximum possible acceleration of the insect can be \[\text{2 }m/{{s}^{2}}\]
C. the insect can move with a constant velocity  
D. the insect cannot move with a constant velocity
Answer» D. the insect cannot move with a constant velocity
2241.

If u be the coefficient of friction between the block and the cart, horizontal acceleration of the cart that is required to prevent block B from faffing is:              

A. \[\mu /g\]
B. \[g/\mu \]
C. \[g\]
D. \[\left( {{\mu }^{2}}+1 \right)g\]
Answer» C. \[g\]
2242.

A block of mass m = 2 kg is placed on a plank of mass \[M=10\text{ }kg\]which is placed on a smooth horizontal plane. The coefficient of friction between the block and the plank is\[\mu =\frac{1}{3}\]. If a horizontal force F is applied on the plank, then find the maximum value of F for which the block and the plank move together. (Take \[g=10\text{ }m/{{s}^{2}}\])

A. 30 N  
B. 40 N
C. 120 N             
D. None of the above
Answer» B. 40 N
2243.

A given object takes n times as much time to slide down a \[45{}^\circ \] rough incline as it takes to slide down a perfectly smooth\[45{}^\circ \]incline. The coefficient of friction between the object and the incline is

A. \[\left( 1-1/{{n}^{2}} \right)\]
B. \[1/\left( 1-{{n}^{2}} \right)\]
C. \[\sqrt{\left( 1-1/{{n}^{2}} \right)}\]
D. \[1/\sqrt{\left( 1-{{n}^{2}} \right)}\]
Answer» B. \[1/\left( 1-{{n}^{2}} \right)\]
2244.

The two blocks, \[m=10\text{ }kg\]and \[M=50\text{ }kg\]are free to move as shown. The coefficient of static friction between the blocks is 0.5 and there is no friction between M and the ground. A minimum horizontal force F is applied to hold m against M that is equal to

A. 100 N
B. 50 N
C. 240 N
D. 180 N
Answer» D. 180 N
2245.

A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied to B for the blocks to move together will be:

A. 30 N
B. 25 N
C. 27 N
D. 48 N
Answer» D. 48 N
2246.

A body starts from rest on a long inclined plane of slope\[45{}^\circ \]. The coefficient of friction between the body and the plane varies as\[u=0.3\text{ }x\], where \[x\]is distance travelled down the plane. The body will have maximum speed (For\[g=10\text{ }m/{{s}^{2}}\]) when \[x=\]

A. 9.8 m    
B. 27 m
C. 12 m    
D. 3.33 m
Answer» E.
2247.

The minimum force required to start pushing a body up rough (frictional coefficient u) inclined plane is \[{{F}_{1}}\]while the minimum force needed to prevent it from sliding down is\[{{F}_{2}}\]. If the inclined plane makes an angle \[\theta \] from the horizontal such that\[\tan \theta =2\mu \] then the ratio \[\frac{{{F}_{1}}}{{{F}_{2}}}\] is

A. 1         
B. 2     
C. 3         
D. 4
Answer» D. 4
2248.

A block is placed on a rough inclined plane. The angle of the incline,\[\theta \] is slowly increased from the horizontal position. At a certain angle, the block starts to slide along the plane. The angle of the incline is increased further. Consider the following graphs: (I)           (II) (III)       (IV) Which of the above graphs correctly depicts the variation of the fractional force, f, exerted by the plane on the block, as a function of\[\theta \]? (Assume that the block does not topple.)

A. I        
B. II
C. III
D. IV
Answer» C. III
2249.

Two identical smooth surfaced solid cylinders of radius r are placed touching along their lengths on a horizontal surface. A third cylinder of same material but twice the radius of that of the cylinders is placed lengthwise on them so that the system remains at rest. If all three cylinders have the same length, then minimum value of the coefficient of friction between smaller cylinders and the surface is:          

A. \[\frac{1}{\sqrt{2}}\]  
B. \[\frac{1}{3}\]
C. \[\frac{1}{3\sqrt{2}}\]  
D. None of these
Answer» D. None of these
2250.

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car.  The car is moving with constant acceleration a directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration a vertically. The tension in the string is equal to               

A. \[m\sqrt{{{g}^{2}}+{{a}^{2}}}\]  
B. \[m\sqrt{{{g}^{2}}+{{a}^{2}}}-ma\]
C. \[m\sqrt{{{g}^{2}}+{{a}^{2}}}+ma\]           
D. \[m\left( g+a \right)\]
Answer» D. \[m\left( g+a \right)\]