A block of mass m moving at a velocity v collides with another block of mass 2m at rest. The lighter block comes to rest after collision. Find the coefficient of restitution.

(a) $\frac{1}{2}$                                               (b) $1$

(c) $\frac{1}{3}$                                               (d) $\frac{1}{4}$

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A small mass attached to a string rotates on a frictionless table top as shown. If the tension on the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

(a) Increase by a factor of 4                                       (b) Decrease by a factor of 2

(c) Remain constant                                                   (d) Increase by a factor of 2

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A particle is moving in a circular orbit with constant speed. Select wrong alternate

1. Its linear momentum is conserved

2. Its angular momentum is conserved

3. It is moving with variable velocity

4. It is moving with variable acceleration

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One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA and IB such that

1. ${\mathrm{I}}_{\mathrm{A}}={\mathrm{I}}_{\mathrm{B}}$

2. ${\mathrm{I}}_{\mathrm{A}}>{\mathrm{I}}_{\mathrm{B}}$

3. ${\mathrm{I}}_{\mathrm{A}}<{\mathrm{I}}_{\mathrm{B}}$

4. $\frac{{\mathrm{I}}_{\mathrm{A}}}{{\mathrm{I}}_{\mathrm{B}}}=\frac{{d}_{A}}{{d}_{B}}$

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A couple produces [NTSE 1995; CBSE PMT 1997; DCE 2004]

(1) Purely linear motion

(2) Purely rotational motion

(3) Linear and rotational motion

(4) No motion

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A particle of mass 1 kg is kept at (1m, 1m, 1m). The moment of inertia of this particle about z-axis would be

1.

2.

3.

4.  None of these

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One quarter sector is cut from a uniform circular disc of radius R.  This sector has mass M.  It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc.  Its moment of inertia about the axis of rotation is [IIT-JEE (Screening) 2001]

(1) $\frac{1}{2}M{R}^{2}$

(2) $\frac{1}{4}M{R}^{2}$

(3) $\frac{1}{8}M{R}^{2}$

(4) $\sqrt{2}M{R}^{2}$

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A wheel is rotating at the rate of 33 rev/min.  If it comes to stop in 20 s. Then, the angular retardation will be

(1) $\mathrm{\pi }\frac{\mathrm{rad}}{{\mathrm{s}}^{2}}$                          (2)

(3)               (4)