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Q. No.

Two equal masses initially moving along the same straight line with velocity \(+4\) m/s and \(-5\) m/s respectively collide elastically. Their respective velocities after the collision will be:

1. \(-5\) m/s and \(+3\) m/s 2. \(+4\) m/s and \(-4\) m/s
3. \(-4\) m/s and \(+4\) m/s 4. \(-5\) m/s and \(+4\) m/s
Subtopic:  Collisions |
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Level 1: 80%+
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A block of mass \(1~\text{kg}\) is given an initial velocity of \(2~\text{m/s}\) towards a \(2~\text{kg}\) block, which is initially at rest. The coefficient of restitution \((e),\) between the blocks, during their collision is \({\Large\frac{1}{2}}.\)

The momentum of the system, as a result of the collision:
1. increases
2. decreases
3. remains constant
4. decreases suddenly and then increases
Subtopic:  Collisions |
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Two blocks, moving towards each other with velocities \(1~\text{m/s}\) and \(4~\text{m/s}\) collide and come to rest, immediately thereafter. Their masses are in the ratio:
1. \(1:4\) 2. \(4:1\)
3. \(2:1\) 4. \(16:1\)
Subtopic:  Collisions |
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A block \((A)\) of mass \(1~\text{kg}\) collides head-on with a stationary block \((B)\) of mass \(2~\text{kg}\) lying on a frictionless horizontal plane. The incoming block \((A)\) has a velocity of \(3~\text{m/s}\) before collision.
                                 
If the coefficient of restitution for the collision is \(e=\dfrac12,\) the final relative speed between the blocks is:
1. \(3~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(1.5~\text{m/s}\)
4. \(1~\text{m/s}\)
Subtopic:  Collisions |
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Level 1: 80%+
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A particle of mass \(m\) collides with another particle of mass \(m',\) which is at rest and the combined mass moves with \(10\text{%}\) reduction in velocity. The ratio of the masses is:
1. \(\dfrac{m'}{m}=\dfrac{1}{10}\) 2. \(\dfrac{m'}{m}=\dfrac{1}{9}\)
3. \(\dfrac{m'}{m}=\dfrac{1}{8}\) 4. \(\dfrac{m'}{m}=\dfrac{1}{2}\)
Subtopic:  Collisions |
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A bomb of mass \(9~\text{kg},\) initially at rest, explodes into two pieces of masses \(3~\text{kg}\) and \(6~\text{kg}.\) The velocity of mass \(3~\text{kg}\) is \(16~\text{m/s}.\) The kinetic energy of mass \(6~\text{kg}\) in joule is:
1. \(46\)
2. \(384\)
3. \(192\)
4. \(768\)
Subtopic:  Collisions |
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A \(5\) kg stationary bomb explodes in three parts with masses in the ratio \(1:1:3\) respectively. If parts having the same mass move in perpendicular directions with velocity \(30\) m/s, then the speed of the bigger part will be:

1. \(10\sqrt{2}~\text{m/s}\) 2. \(\dfrac{10}{\sqrt{2}}~\text{m/s}\)
3. \(13\sqrt{2}~\text{m/s}\) 4. \(\dfrac{15}{\sqrt{2}}~\text{m/s}\)
Subtopic:  Collisions |
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Level 1: 80%+
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A particle of mass \(m\) moving with velocity \(v\) collides with a stationary particle of mass \(2m\) and sticks to it. The velocity of the combined mass (system) will be:
1. \(v\) 2. \(\dfrac{v}{2}\)
3. \(\dfrac{v}{3}\) 4. \(\dfrac{v}{4}\)
Subtopic:  Collisions |
 84%
Level 1: 80%+
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An object of mass \(m,\) moving with a speed \(v,\) collides with a stationary object of mass \(M\) & gets linked with it to form a single object. The loss of kinetic energy, during this collision, equals the potential energy stored in a spring (spring constant \(k\)). When its normal length is changed by an amount \(x,\) the value of \(x\) equals:
1. \(v\left[\dfrac{mM}{(k(m+M)}\right]^{1/2}\)

2. \(v\left[\dfrac{mM}{(k(m-M)}\right]^{1/2}\)

3. \(\left[\dfrac{vkmM}{m+M}\right]^{1/2}\)

4. \(\left[\dfrac{vkmM}{m-M}\right]^{1/2}\)
Subtopic:  Collisions |
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A body at rest breaks into two pieces of equal masses. The parts will move:

1. in the same direction.
2. along different lines.
3. in opposite directions with equal speeds.
4. in opposite directions with unequal speeds.

Subtopic:  Collisions |
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