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

2006 4 questions

1. Q492006 · 29 Apr 2006 · Shift 1

   Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the center of mass through a distance $d$, by what distance should the second particle is moved, so as to keep the center of mass at the same position?

   1. A.$\frac{m_2}{m_1}d$
   2. B.$\frac{m_1}{m_1+m_2}d$
   3. C.$\frac{m_1}{m_2}d$
   4. D.$d$
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   Answer: C

2. Q502006 · 29 Apr 2006 · Shift 1

   Four point masses, each of value $m$, are placed at the corners of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is

   1. A.$2m{l}^2$
   2. B.$\sqrt{3}m{l}^2$
   3. C.$3m{l}^2$
   4. D.$m{l}^2$
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   Answer: C

3. Q512006 · 29 Apr 2006 · Shift 1

   A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ${\omega }^{\prime }=$

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

4. Q572006 · 29 Apr 2006 · Shift 1
   
   1. A.$F(\hat{i}-\hat{j})$
   2. B.$-F(\hat{i}+\hat{j})$
   3. C.$F(\hat{i}+\hat{j})$
   4. D.$-F(\hat{i}-\hat{j})$
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   Answer: B