Point masses 1,  2,  3  and  4 kg are lying a

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 Multiple Choice QuestionsMultiple Choice Questions

141.

The speed of earth's rotation about its axis is o. Its speed is increased to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is

  • 1

  • 8.5

  • 17

  • 34


142.

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

  • MR2

  • 12 MR2

  • 32 MR2

  • 72 MR2


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143.

Point masses 1,  2,  3  and  4 kg are lying at the points (0, 0, 0),  (2, 0, 0),  (0, 3, 0)  and  (- 2, -2, 0)   respectively. The moment-of inertia of this system about  X-axis  will be

  • 43 kg-m2

  • 34  kg-m2

  • 27  kg-m2

  • 72  kg-m2


A.

43 kg-m2

Moment of inertia of the whole system about the axis of rotation will be equal to the sum of the moments of inertia of all the particles.

     

           I = I1 + I2 + I3 + I4

           I = m1 r12 + m2 r22 + m3 r32 + m4 r42

           I = ( 1 × 0 ) + ( 2 × 0 ) + ( 3 × 32 ) + 4 (-2 )2

           I = 0 + 0 + 27 + 16

           I = 43 kg-m3  


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144.

The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then, its radius of gyration about a parallel axis through its centre of mass will be

  • 80 cm

  • 8 cm

  • 0.8 cm

  • 80 m


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145.

A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad-s-2 produced in it due to the torque. Then, moment of inertia of the wheel is (g =10 ms-2 )

  • 2 kg-m2

  • 1 kg-m2

  • 4 kg-m2

  • 8 kg-m2


146.

An object start sliding on a frictionless inclined plane and from same height another object start falling freely.

  • both will reach with same speed

  • both will reach with same acceleration

  • both will reach in same time

  • None of the above


147.

Two rigid bodies A and B rotate with rotational kinetic energies E, and E, respectively. The moments of inertia of A and B about the axis of rotation are IA and IB respectively.

If IA = IB2 and  EA = 100 = EB, the ratio of angular momentum (LA ) of A to the angular  momentum ( LB ) of B is

  • 25

  • 5/4

  • 5

  • 1/4


148.

The working principle of a ball point pen is

  • Bernoulli's theorem

  • surface tension

  • gravity

  • viscosity


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149.

Progressive waves are represented by the equation y1 = a sin (ωt - x )  and y2 = bcos (ωt - x ).  The phase difference wave is

  • 0o

  • 45o

  • 90o

  • 180o


150.

If applied torque on a system is zero, i.e.,Τ = 0 , then for that system

  • ω = 0

  • α = 0

  • J = 0

  • F = 0


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