IIT JEE Entrance Question

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Radius of gyration of a body does not depend on

a) Area of the body

b) Axis of rotation

c) Translation motion

d) Shape of the body

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What should be the minimum coefficient of static friction between the plane and the cylinder, for the cylinder not to slip on an inclined plane?

a) 13 sinθ

b) 23 sinθ

c) 23 tanθ

d) 13 tanθ

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The moment of inertia of a solid cylinder about its axis is I. It is allowed to roll down an inclined plane without slipping. If its angular velocity at the bottom beω , then the kinetic energy of the cylinder will be:

a) 32Iω2

b) 2Iω2

c) 12Iω2

d) Iω2

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A circular disc is rolling on a horizontal plane. Its total kinetic energy is 150 J. What is its translational KE?

a) 125J

b) 100J

c) 150J

d) 200J

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A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

a) Depends on their masses

b) Sphere

c) Disc

d) Both reach at the same time

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Resonating structures of molecules have:

a) the different number of paired and unpaired electrons

b) identical bonding

c) identical arrangement of atoms and nearly same energies

d) different bonding

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A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The

rate at which internal energy of the system increase is

(1)500 W

(2) 600 W

(3) 800 W

(4) 1200 W

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A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of

spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with

constant angular velocity 5 rad/s about point A, then tension in the spring is –

(1) 0.75 N

(2) 1.5 N

(3) 0.25 N

(4) 0.50 N

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A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly

distributed across this cross-section. The magnetic field is

(1) zero in the region r < a and inversely proportional to r in the region r > a

(2) inversely proportional to r in the region r < a and uniform throughout in the region r > a

(3) directly proportional to r in the region r < a and inversely proportional to r in the region r > a

(4) uniform in the region r < a and inversely proportional to distance r from the axis, in the region r > a