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AI Gen: Mechanics - Advanced (Rotational, SHM) question bank (Physics)

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Q1.

A uniform solid cylinder of mass M and radius R rolls without slipping down an inclined plane of inclination theta. A string is wound around the cylinder and its free end is fixed to a rigid support parallel to the incline. The tension in the string is:

Topic: Mechanics - Advanced (Rotational, SHM) | Source: AI Generated (JEE Advanced)

(A)

Mg sin(theta) / 3

(B)

Mg sin(theta) / 2

(C)

2Mg sin(theta) / 3

(D)

Mg sin(theta)

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Q2.

A uniform thin rod of mass M and length L is hinged at one end and allowed to oscillate in a vertical plane. A particle of mass m is attached to its free end. The time period of small oscillations of this system is:

Topic: Mechanics - Advanced (Rotational, SHM) | Source: AI Generated (JEE Advanced)

(A)

2*pi * sqrt((M + 3m)L / (3(M + 2m)g))

(B)

2*pi * sqrt((M + m)L / (3(M + 2m)g))

(C)

2*pi * sqrt((4M + 3m)L / (3(M + m)g))

(D)

2*pi * sqrt((M + 3m)L / (M + m)g)

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