Q. No.A particle of mass \(m\) moving in the \(x\)-direction with speed \(2v\) is hit by another particle of mass \(2m\) moving in the \(y\)-direction with speed \(v.\) If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:
1. \(44\%\)
2. \(50\%\)
3. \(56\%\)
4. \(62\%\)
1. \({mv^2\over 2(L-nr)}\)
2. \({mv^2\over L-2nr}\)
3. \({mv^2\over L-nr}\)
4. zero
1. \(\tan\theta=\dfrac{\sqrt3+\sqrt2}{1-\sqrt2} \)
2. \(\tan\theta=\dfrac{1-\sqrt3}{1+\sqrt2}\)
3. \(\tan\theta=\dfrac{\sqrt3-\sqrt2}{1-\sqrt2}\)
4. \(\tan\theta=\dfrac{1-\sqrt3}{\sqrt2(1+\sqrt3)}\)
In a collinear collision, a particle with an initial speed \(v_0\) strikes a stationary particle of the same mass. If the final total kinetic energy is \(50\%\) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:
1. \(\frac{{v_0}}{4}\)
2. \(\sqrt{2}{v_0}\)
3. \(\frac{{v_0}}{2}\)
4. \(\frac{{v_0}}{\sqrt{2}}\)
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is \(P_d\); while for its similar collision with carbon nucleus at rest, fractional loss of energy is \(P_c\). The values of \(P_d\) and \(P_c\) are respectively:
1. \(0.89,~0.28\)
2. \(0.28, ~0.89\)
3. \(0,~0\)
4. \(0,~1\)
A body of mass \(m_1\) moving with an unknown velocity of \(v_1 \hat{i},\), undergoes a collinear collision with a body of mass \(m_2\) moving with a velocity \(v_2\hat{i}.\). After collision, \(m_1\) and \(m_2\) move with velocities of \(v_3\hat{i}\) and \(v_4\hat{i},\) respectively . If \(m_2=0.5m_1\) and \(v_3=0.5v_1\), then \(v_1\) is:
1. \( v_4-\frac{v_2}{4} \)
2. \( v_4+v_2 \)
3. \( v_4-\frac{v_2}{2} \)
4. \( v_4-v_2\)
A body of mass \(2~\text{kg}\) makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?
1. \(1.5~\text{kg}\)
2. \(1.2~\text{kg}\)
3. \(1.0~\text{kg}\)
4. \(1.8~\text{kg}\)
| 1. | \(\sqrt{2}v\) | 2. | \(\dfrac{v}{2\sqrt{2}}\) |
| 3. | \(\dfrac{v}{\sqrt{2}}\) | 4. | \(2\sqrt{2}v\) |
Two particles, of masses \(M\) and \(2M\), moving, as shown, with speeds of \(10~\text{m/s}\) and \(5~\text{m/s}\), collide elastically at the origin. After the collision, they move along the indicated directions with speeds \(v_1\) and \(v_2\), respectively. The values of \(v_1\) and \(v_2\) are nearly:
| 1. | \(3.2~\text{m/s}~\text{and}~12.6~\text{m/s}\) |
| 2. | \(3.2~\text{m/s}~\text{and}~6.3~\text{m/s}\) |
| 3. | \(6.5~\text{m/s}~\text{and}~6.3~\text{m/s}\) |
| 4. | \(6.5~\text{m/s}~\text{and}~3.2~\text{m/s}\) |
1. \(5\)
2. \(2\)
3. \(4\)
4. \(3\)
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