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Q. No.A body of
(given, \(R=14\) m, \(g=10\) m/s2 and \(\sqrt{2}=1.4\))
1. \(21.9\) m/s
2. \(10.6\) m/s
3. \(19.8\) m/s
4. \(16.7\) m/s
Subtopic: Conservation of Mechanical Energy |
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Level 2: 60%+
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A stationary particle breaks into two parts of masses \(\mathrm{m_A}\) and \(\mathrm{m_B}\) which move with velocities \(\mathrm{v_A}\) and \(\mathrm{v_B}\) respectively. The ratio of their kinetic energies \(\mathrm{(K_B:K_A)}\) is:
1. \(\mathrm{m_B:m_A}\)
2. \(1:1\)
3. \(\mathrm{m_Bv_B:m_Av_A}\)
4. \(\mathrm{v_B:v_A}\)
1. \(\mathrm{m_B:m_A}\)
2. \(1:1\)
3. \(\mathrm{m_Bv_B:m_Av_A}\)
4. \(\mathrm{v_B:v_A}\)
Subtopic: Collisions |
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Level 3: 35%-60%
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A force \(\left(3 x^2+2 x-5\right)~\text N\) displaces a body from \(x = 2~\text m\) to \(x = 4~\text m.\) Work done by this force is: ________ J.
1. \(64~\text J\)
2. \(36~\text J\)
3. \(58~\text J\)
4. \(87~\text J\)
1. \(64~\text J\)
2. \(36~\text J\)
3. \(58~\text J\)
4. \(87~\text J\)
Subtopic: Work Done by Variable Force |
92%
Level 1: 80%+
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A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation \(\begin{equation} v=\alpha \sqrt{x} \end{equation}\), where \(\begin{equation} \alpha \end{equation}\) is a constant. The total work done by all the forces applied on the particle during its displacement from \(x=0\) to \(x=d\), will be :
1. \(\begin{equation} \frac{m}{2 \alpha^2 d} \end{equation}\)
2. \(\begin{equation} \frac{m d}{2 \alpha^2} \end{equation}\)
3. \(\begin{equation} \frac{m \alpha^2 d}{2} \end{equation}\)
4. \(\begin{equation} 2 m \alpha^2 d \end{equation}\)
1. \(\begin{equation} \frac{m}{2 \alpha^2 d} \end{equation}\)
2. \(\begin{equation} \frac{m d}{2 \alpha^2} \end{equation}\)
3. \(\begin{equation} \frac{m \alpha^2 d}{2} \end{equation}\)
4. \(\begin{equation} 2 m \alpha^2 d \end{equation}\)
Subtopic: Work Done by Variable Force |
86%
Level 1: 80%+
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A bullet of mass \(50 ~\text g\) is fired with a speed \(100 ~\text{m/s}\) on a plywood and emerges with \(40 ~\text{m/s}.\) The percentage loss of kinetic energy is :
1. \(44\%\)
2. \(32\%\)
3. \(84\%\)
4. \(16\%\)
1. \(44\%\)
2. \(32\%\)
3. \(84\%\)
4. \(16\%\)
Subtopic: Work Energy Theorem |
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Level 1: 80%+
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A bob of mass m is suspended at a point \(O\) by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity \(v_0\) at the point A the string becomes slack when, the bob reaches at the point \(D\). The ratio of the kinetic energy of the bob at the points \(B\) and \(C\) is _____.
1. \(3\)
2. \(1\)
3. \(4\)
4. \(2\)
1. \(3\)
2. \(1\)
3. \(4\)
4. \(2\)
Subtopic: Conservation of Mechanical Energy |
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Level 2: 60%+
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A force \(\vec F = 2 \hat i + b \hat j + \hat k\) is applied on a particle and it undergoes a displacement \(\hat i - 2 \hat j - \hat k.\) What will be the value of \(b,\) if work done on the particle is zero
1. \(2\)
2. \(0\)
3. \(\dfrac{1}{3}\)
4. \(\dfrac{1}{2}\)
1. \(2\)
2. \(0\)
3. \(\dfrac{1}{3}\)
4. \(\dfrac{1}{2}\)
Subtopic: Work done by constant force |
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Level 1: 80%+
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A body of mass \(m\) connected to a massless and unstretchable string goes in vertical circle of radius \(R \) under gravity \(g.\) The other end of the string is fixed at the centre of circle. If velocity at top of circular path is \(n \sqrt{gR} \), where, \(n>1 \), then ratio of kinetic energy of the body at bottom to that at top of the circle is:
1. \(\dfrac{n+4}{n}\)
2. \(\dfrac{n^2}{n^2+4}\)
3. \(\dfrac{n}{n+4}\)
4. \(\dfrac{n^2+4}{n^2}\)
1. \(\dfrac{n+4}{n}\)
2. \(\dfrac{n^2}{n^2+4}\)
3. \(\dfrac{n}{n+4}\)
4. \(\dfrac{n^2+4}{n^2}\)
Subtopic: Conservation of Mechanical Energy |
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A body of mass \(100~\text g\) is moving in a circular path of radius \(2~\text m\) on a vertical plane as shown in the figure. The velocity of the body at point \(A\) is \(10~\text{m/s}.\) The ratio of its kinetic energies at point \(B\) and \(C\) is: \((\text{use}~g=9.8~\text{m/s}^{2})\)
| 1. | \(\dfrac{2+\sqrt{2}}{3} \) | 2. | \(\dfrac{3+\sqrt{3}}{2} \) |
| 3. | \(\dfrac{2+\sqrt{3}}{3} \) | 4. | \(\dfrac{3-\sqrt{2}}{2}\) |
Subtopic: Conservation of Mechanical Energy |
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Level 3: 35%-60%
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A ball of mass \(100~\text g\) is projected with a velocity of \(20~\text{m/s}\) at an angle of \(60^\circ\) above the horizontal. What is the decrease in its kinetic energy as it moves from the point of projection to the highest point of its trajectory?
1. \(20~\text{J}\)
2. \(5~\text{J}\)
3. zero
4. \(15~\text{J}\)
1. \(20~\text{J}\)
2. \(5~\text{J}\)
3. zero
4. \(15~\text{J}\)
Subtopic: Concept of Work |
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Level 2: 60%+
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