Centre of Mass & Rotational Motion · JEE Main previous year questions

2002 6 questions

1. Q832002 · 27 Apr 2002 · Shift 1

   Initial angular velocity of a circular disc of mass $M$ is ${\omega }_1$. Then two small spheres of mass $m$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

   1. A.$\left(\frac{M+m}{M}\right){\omega }_1$
   2. B.$\left(\frac{M+m}{m}\right){\omega }_1$
   3. C.$\left(\frac{M}{M+4m}\right){\omega }_1$
   4. D.$\left(\frac{M}{M+2m}\right){\omega }_1$
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   Answer: C

2. Q852002 · 27 Apr 2002 · Shift 1

   A cylinder of height $20\mathrm{m}$ is completely filled with water. The velocity of efflux of water (in $\mathrm{m}{\mathrm{s}}^{-1}$) through a small hole on the side wall of the cylinder near its bottom is

   1. A.$10$
   2. B.$20$
   3. C.$25.5$
   4. D.$5$
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   Answer: B

3. Q862002 · 27 Apr 2002 · Shift 1

   Two identical particles move towards each other with velocity $2v$ and $v$ respectively. The velocity of center of mass is

   1. A.$v$
   2. B.$v/3$
   3. C.$v/2$
   4. D.zero
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   Answer: C

4. Q872002 · 27 Apr 2002 · Shift 1

   A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

   1. A.solid sphere
   2. B.hollow sphere
   3. C.ring
   4. D.all same
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   Answer: D

5. Q882002 · 27 Apr 2002 · Shift 1
   
   1. A.$mvL$
   2. B.$mvl$
   3. C.$mvr$
   4. D.zero
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   Answer: D

6. Q1032002 · 27 Apr 2002 · Shift 1

   Moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is

   1. A.$\frac{M{R}^2}{2}$
   2. B.$M{R}^2$
   3. C.$2M{R}^2$
   4. D.$\frac{M{R}^2}{4}$
   Show answer

   Answer: A