Three points charges +q, -2q and +q are placed at points (x=

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 Multiple Choice QuestionsMultiple Choice Questions

151.

The potential energy of particle varies with distance x fixed a origin as v = Axx + B; where A and B are constants. The dimensions of AB are

  • [ M L5/2 T-2 ]

  • [ M L2 T-2 ]

  • [ M3/2 L3/2 T-2 ]

  • [M L7/2 T-2 ]


152.

A solid sphere and a hollow sphere of the same material and of a same size can be distinguished without weighing

  • by determining their moments of inertia about their coaxial axe

  • by rolling them simultaneously on an inclined plane

  • by rotating them about a common axis of rotation

  • by applying equal torque on them


153.

A certain vector in the xy-plane has an x-component of 4 m and a y-component of 10 m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component is (approximately)

  • 20 m

  • 7.2 m

  • 5.0 m

  • 4.5 m


154.

A coin is dropped in a lift. It takes time t1  to reach the floor when lift is stationary. It takes time t2 when lift is moving up with constant acceleration. Then,

  • t1 ≥ t2

  • t2 > t1

  • t1 = t2

  • t1 >> t2


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155.

A body is thrown with a velocity of 9.8 m/s making an angle of 30° with the horizontal. It will hit the ground after a time

  • 1.5 s

  • 1 s

  • 3 s

  • 2 s


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156.

Three points charges +q, -2q and +q are placed at points (x=0,  y=a,  z=0),  ( x=0,  y=0,  z=0 )  and  (x=a,  y=0,  z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

  • √2 qa along + y direction

  • √2 qa along the line joining point

  • qa along the line joining points (x = 0,y = 0, z = 0) and (x = a, y = a, z = 0)

  • √2 qa along + x direction


B.

√2 qa along the line joining point

0 is the origin at which -2q charge is placed. The system is equivalent to two dipoles along x and y-directions respectively. The dipole moments of two dipoles are shown in figure

The resultant dipole moment will be directed along OP where P = (a, a, 0). The magnitude of resultant dipole moment is


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157.

The angle between two linear transmembrane domains is defined by following vectors a = i^ + j^ - k^ and  b = i^ - j^  +  k^

  • cos-1 13

  • cos-1 -13

  • sin-1 -13

  • sin-1 13


158.

A projectile is fired with a velocity u at angle θ with the ground surface. During the motion at any time it is making an angle a with the ground surface. The speed of particle at this time will be

  • ucosθ secα

  • ucosθ tanα

  • u2 cos2α sin2α

  • usinθ.sinα


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159.

Water level is maintained in a cylindrical vessel upto a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?

      

  • h = H2

  • h = 3H2

  • h = 2 H3

  • h = 34H


160.

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?


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