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Q. No.The power of a crane, which lifts a mass of \(1000\) kg to a height of \(20\) m in \(10\) s is: (\(g=9.8~\) m/s2)
1. \(19.6\) W
2. \(39.2\) W
3. \(39.2\) kW
4. \(19.6\) kW
1. \(19.6\) W
2. \(39.2\) W
3. \(39.2\) kW
4. \(19.6\) kW
Subtopic: Power |
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Bob \(B\) of mass \(m\) at rest is hanging vertically from the ceiling via a massless string of length \(10~\text{m},\) as shown in the figure. Point mass \(A\) of mass \(m\) travelling horizontally with speed \(10\) m/s hits bob \(B\) elastically. The bob \(B\) rises \(h\) meter after the collision. Taking the acceleration due to gravity \(g=10\) m/s2 and neglecting the size of the bob, the value of \(h\) is:
1. \(2.5\)
2. \(8\)
3. \(7\)
4. \(5\)
1. \(2.5\)
2. \(8\)
3. \(7\)
4. \(5\)
Subtopic: Collisions |
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A particle of mass \(M\) moves along a horizontal \(x\) axis from \(x = 0\) to \(x = L.\) The coefficient of kinetic friction varies as a function of \(x\) as \(\mu_k(x) = \mu_0 - \alpha x ,\) where \(\mu_0\) and \(\alpha\) are constants of appropriate dimensions, so that \(\mu _k(L) = 0.\) The total work done by the frictional force during the motion is \(n\mu_0MgL ,\) where \(g\) is the acceleration due to gravity. The value of \(n\) is:
1. \(\dfrac{1}{2}\)
2. \(3\)
3. \(1\)
4. \(\dfrac{1}{3}\)
1. \(\dfrac{1}{2}\)
2. \(3\)
3. \(1\)
4. \(\dfrac{1}{3}\)
Subtopic: Work Done by Variable Force |
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The kinetic energies of two similar cars \(A\) and \(B\) are \(100~\text J\) and \(225~\text J\) respectively. On applying brakes, car \(A\) stops after \(1000~\text m\) and car \(B\) stops after \(1500~\text m.\) If \(F_A\) and \(F_B\) are the forces applied by the brakes on cars \(A\) and \(B,\) respectively, then the ratio \(\dfrac{F_A}{F_B}\) is:
| 1. | \(\dfrac{1}{3}\) | 2. | \(\dfrac{1}{2}\) |
| 3. | \(\dfrac{3}{2}\) | 4. | \(\dfrac{2}{3}\) |
Subtopic: Work Energy Theorem |
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NEET - 2025
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A bob of heavy mass \(m\) is suspended by a light string of length \(l.\) The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point \(P\) making an angle \(\theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point \(P\) to its initial speed \(v_0\) is:
| 1. | \(\left(\dfrac{\cos \theta}{2+3 \sin \theta}\right)^{-1 / 2}\) | 2. | \(\left(\dfrac{\sin \theta}{2+3 \sin \theta}\right)^{1 / 2}\) |
| 3. | \((\sin \theta)^{1 / 2}\) | 4. | \(\left(\dfrac{1}{2+3 \sin \theta}\right)^{1 / 2}\) |
Subtopic: Conservation of Mechanical Energy |
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Two bodies \(A\) and \(B\) of the same mass undergo completely inelastic one-dimensional collision. The body \(A\) moves with velocity \(v_1\) while the body \(B\) is at rest before collision. The velocity of the system after collision is \(v_2.\) The ratio of \(v_1:v_2\) is:
1. \(2:1\)
2. \(4:1\)
3. \(1:4\)
4. \(1:2\)
1. \(2:1\)
2. \(4:1\)
3. \(1:4\)
4. \(1:2\)
Subtopic: Collisions |
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At any instant of time \(t,\) the displacement of any particle is given by \(2t-1\) (SI unit) under the influence of the force of \(5~\text N.\) The value of instantaneous power (in SI units) is:
| 1. | \(5\) | 2. | \(7\) |
| 3. | \(6\) | 4. | \(10\) |
Subtopic: Power |
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The object \(A\) has half the kinetic energy as that of the object \(B.\) The object \(B\) has half the mass as that of the object \(A.\) The object \(A\) speeds up by \(1~\text{ms}^{-1}\) and then has the same kinetic energy as that of the object \(B.\) The initial speed of the object \(A\) is:
(Take \(\sqrt2\cong1.4\))
(Take \(\sqrt2\cong1.4\))
| 1. | \(0.5~\text{ms}^{-1}\) | 2. | \(1~\text{ms}^{-1}\) |
| 3. | \(2.5~\text{ms}^{-1}\) | 4. | \(4.8~\text{ms}^{-1}\) |
Subtopic: Work Energy Theorem |
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A particle is displaced through \((3 \hat{i}+4 \hat{j})~\text{m}\) by force \(2 \hat{i}~\text{N}\). The work done is:
1. \(14~\text{J}\)
2. \(8~\text{J}\)
3. \(6~\text{J}\)
4. \(10~\text{J}\)
1. \(14~\text{J}\)
2. \(8~\text{J}\)
3. \(6~\text{J}\)
4. \(10~\text{J}\)
Subtopic: Work done by constant force |
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An object is moving along the horizontal \(x\text-\)direction with an initial kinetic energy of \(10~\text J.\) It is displaced through \(x=(3\hat{i})~\text{m}\) under the influence of a force \(\vec{{{F}}}=(-2\hat{i}+3\hat{j})~\text N.\) The kinetic energy of the object at the end of the displacement \(x\) is:
| 1. | \(10~\text{J}\) | 2. | \(16~\text J\) |
| 3. | \(4~\text J\) | 4. | \(6~\text J\) |
Subtopic: Work Energy Theorem |
68%
Level 2: 60%+
NEET - 2024
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