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Q. No.If a force \(F \) applied on an object moving along the \(y\)-axis varies with the \(y\)-coordinate as \(F=3+2y^{2}. \) The work done in displacing the body from \(y=2\text{ m}\) to \(y=5\text{ m}\) is:
1. \(87\text{ J}\)
2. \(0 \)
3. \(57\text{ J}\)
4. \(72\text{ J}\)
Subtopic: Work Done by Variable Force |
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Bob \(\mathrm{P}\) is released from the position of rest at the moment shown. If it collides elastically with an identical bob \(\mathrm{Q}\) hanging freely then the velocity of \(\mathrm{Q}\) just after the collision is: (Take \(g=10\) m/s2 )
1. \(4\) m/s
2. \(4\) cm/s
3. \(2\) m/s
4. \(2\) cm/s
1. \(4\) m/s
2. \(4\) cm/s
3. \(2\) m/s
4. \(2\) cm/s
Subtopic: Collisions |
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A particle of mass \(m\) is moving under a force whose delivered power \(P\) is constant. The initial velocity of the particle is zero. The position of a particle at \(t=4\) s is:
| 1. | \(\dfrac{16}{3}\sqrt{\dfrac{2P}{m}}\) | 2. | \(\dfrac{4}{3}\sqrt{\dfrac{2P}{m}}\) |
| 3. | \(\dfrac{2}{3}\sqrt{\dfrac{P}{m}}\) | 4. | \(\dfrac{3}{10}\sqrt{\dfrac{P}{m}}\) |
Subtopic: Power |
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What is the initial speed of a \(10~\text{g}\) bullet that strikes a stationary \(200~\text{g}\) ball at a height of \(20\) m, if after the horizontal collision the bullet travels \(120\) m horizontally and the ball travels \(30\) horizontally before hitting the ground (take \(g=10\) m/s²)?
1. \(150\) m/s
2. \(90\) m/s
3. \(240\) m/s
4. \(360\) m/s
1. \(150\) m/s
2. \(90\) m/s
3. \(240\) m/s
4. \(360\) m/s
Subtopic: Collisions |
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A lift of mass \(500\) kg starts moving downwards with an initial speed of \(2\) m/s and accelerates at a rate of \(2~\text{m}/\text{s}^2.\) The kinetic energy of the lift when it has moved \(6~\text{m}\) down, is:
1. \(3\) J
2. \(3\) kJ
3. \(7\) J
4. \(7\) kJ
1. \(3\) J
2. \(3\) kJ
3. \(7\) J
4. \(7\) kJ
Subtopic: Work Energy Theorem |
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A ball was dropped from \(20\) m height from the ground. The height up to which it rises after the collision is: (Use \(e={{1}\over{2}} \) , \(g=10\) m/s2 )
1. \(3\) m
2. \(5\) m
3. \(10\) m
4. \(6\) m
1. \(3\) m
2. \(5\) m
3. \(10\) m
4. \(6\) m
Subtopic: Collisions |
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A constant force acts on a body of mass \(1\) kg, providing it a kinetic energy of \(1800~\text{J}\) by the end of \(5^{\mathrm{th}}\) second. If the body was initially at rest, at the beginning of the action of force, then the magnitude of the force is equal to:
1. \(30~\text{ N}\)
2. \(12~\text{ N}\)
3. \(25~\text{ N}\)
4. \(15~\text{ N}\)
Subtopic: Work Energy Theorem |
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A variable force given by; \(F=5kx \) (in newtons) acts on a body moving along the \(x\)-axis, where \(k\) is a constant.
What is the work done by this force as the body moves from \(x=2~\text{m}\) to \(x=5~\text{m}\)?
What is the work done by this force as the body moves from \(x=2~\text{m}\) to \(x=5~\text{m}\)?
| 1. | \(\left ( \dfrac{205}{2}k \right )\text{J} \) | 2. | \(\left ( \dfrac{105}{2}k \right )\text{J} \) |
| 3. | \((52k)~\text{J}\) | 4. | \((51k)~\text{J}\) |
Subtopic: Work Done by Variable Force |
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An object \(A\) is released from a height h such that the ratio of its speed before striking the ground and after striking the ground is \(4 : 1.\) If loss of kinetic energy is \({{x}\over{4}}\%\) then value of \(x\) is
1. 225
2. 50
3. 375
4. 25
1. 225
2. 50
3. 375
4. 25
Subtopic: Conservation of Mechanical Energy |
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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 |
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