The work done by all the forces (external and internal) on a system equals the change in:

1. total energy 2. kinetic energy
3. potential energy 4. none of these

Subtopic:  Work Energy Theorem |
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A block of \(1\) kg is released from the top of a smooth curve \(\mathrm{AB},\) and then it encounters a rough surface \(\mathrm{BC},\) coming to rest at \(\mathrm{C}.\) The work done by friction is:
(take \(g=10\) m/s2)

1. \(25\) J 2. \(50\) J
3. \(-25\) J 4. \(-50\) J
Subtopic:  Work Energy Theorem |
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The minimum speed that a simple pendulum's bob should be given so that it rises to a level where its string makes \(60^\circ\) with the vertical is:

     

1. \(\sqrt{2gL}\)
2. \(\sqrt{2gL}\) \(\text{cos} 60^\circ\)
3. \(\sqrt{2g(L-L~\text{cos}60^\circ)}\)
4. \(\sqrt{2gL}\) \(\text{sin} 60^\circ\)

Subtopic:  Gravitational Potential Energy |
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A block is suspended from a spring and causes an extension of \(2\) cm. It is now imparted a kinetic energy \(E\) so that the block rises up by exactly \(2\) cm. If the block were to be given the same kinetic energy upward, without being attached to a spring, it would rise up by:
1. \(1\) cm 
2. \(2\) cm 
3. \(4\) cm 
4. \(8\) cm 
Subtopic:  Elastic Potential Energy |
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A block of mass \(m\) moving with a speed \(v\) meets an unextended spring fixed at one end, and having a spring constant \(k.\) During maximum compression, the mid-point of the spring undergoes a rightward displacement \(x\). Then, \(v=\)
         

1. \(\sqrt{\frac{k}{m}}x\)
2. \(\sqrt{\frac{m}{k}}x\)
3. \(\sqrt{\frac{k}{m}}(2x)\)
4. \(\sqrt{\frac{k}{m}}\Big(\frac{x}{2}\Big)\)
Subtopic:  Work Done by Variable Force |
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A particle undergoes an elastic collision with an identical particle at rest. After the collision, the two particles move with velocities \(\overrightarrow{v_1},~\overrightarrow{v_2}\). Final velocities \(\overrightarrow{v_1},~\overrightarrow{v_2}\) are in different directions.
The angle between \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\) is:
1. \(\dfrac{\pi}{6}\) 2. \(\dfrac{\pi}{3}\)
3. \(\dfrac{\pi}{2}\) 4. \(\dfrac{2\pi}{3}\)
Subtopic:  Collisions |
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A block is moved along a horizontal plane by means of a force of constant magnitude of \(5\) N, but acting at an angle \(\theta\) which is proportional to the displacement (\(x\)):    \(\theta=\frac{1}{2} x,\)
where \(x\) is in \(\text{m}\) and \(\theta\) is in radians. The work done by this force until the force becomes vertical is:
                    
1. \(5\) J
2. \(10 \) J
3. \(2.5 \) J
4. \(1.25\) J
Subtopic:  Work Done by Variable Force |
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A horizontal force \(F\) acts on a \(2\) kg block placed on a smooth horizontal plane. It varies with time \(t\) as shown in the figure. The block is initially at rest.
           
The work done by the force until \(t=2\) s, equals:
1. \(6.25 \) J
2. \(4.5 \) J
3. \(2.25 \) J
4. \(1.5\) J
Subtopic:  Work Done by Variable Force |
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A car is driven by an engine that delivers constant power (except possibly at the initial instant). If it starts from rest, its displacement varies with time \((t)\) as:
1. \(t\)
2. \(\sqrt t\)
3. \(\frac{1}{\sqrt t}\)
4. \(t\sqrt t\)
Subtopic:  Power |
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The work done by gravity on a projectile of mass \(m\) fired with a speed \(u\) at an angle \(\theta\) to the horizontal, until the time of impact is:
          
1. zero 2. \(-\frac12mu^2cos^2\theta\)
3. \(-\frac12mu^2sin^2\theta\) 4. \(-\frac12mu^2\)
Subtopic:  Work done by constant force |
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