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A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 πs. The acceleration of the particle is 

  • 25 m/s2

  • 36 m/s2

  • 5 m/s2

  • 5 m/s2


C.

5 m/s2

D.

5 m/s2

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A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in the figure. When a string is cut, the initial angular acceleration of the rod is,

  • 3g / 2L

  • g/L

  • 2g/L

  • 2g/L


A.

3g / 2L

Torque on the rod = moment of weight of the rod about P


              ... (i)
Moment of inertia of rod about,

              ... (ii)
As  = I 
From equations (i) and (ii), we get

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The moment of inertia of a thin uniform rod of mass M  and length L about an axis passing through its mid - point and perpendicular to its length is Io. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

  • Io + ML2/4

  • Io + 2ML2

  • Io + ML2

  • Io + ML2


A.

Io + ML2/4

The theorem of parallel axis for moment of inertia

I = ICM + Mh2


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A small object of uniform density rolls up a curved surface with an initial velocity v'. It reaches up to a maximum height of fraction numerator 3 straight v squared over denominator 4 straight g end fraction with respect to the initial position. The object is,

  • ring

  • solid sphere

  • hollow sphere

  • hollow sphere


D.

hollow sphere

As v = 
Given, h = 

Hence, the object is disc.

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The instantaneous angular position of a point on a rotation wheel is given by the equation 
Q(t)  = 2t3 - 6t2

The torque on the wheel becomes zero at

  • t = 0.5 s 

  • t = 0.25 s

  • t = 2s

  • t = 2s


D.

t = 2s

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