A body of mass \(1\) kg begins to move under the action of a time-dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) \) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along the \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. What power will be developed by the force at the time (\(t\))?
1. \(\left(2 t^2+4 t^4\right) \) W
2. \(\left(2 t^3+3 t^3\right) \) W
3. \(\left(2 t^3+3 t^5\right)\) W
4. \(\left(2 t^3+3 t^4\right) \) W

Subtopic:  Power |
 79%
From NCERT
NEET - 2016
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What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 g R}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{ g R}\)

Subtopic:  Gravitational Potential Energy |
 85%
From NCERT
NEET - 2016
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Two similar springs \(P\) and \(Q\) have spring constants \(k_P\) and \(k_Q\), such that \(k_P>k_Q\). They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs \(W_P\) and \(W_Q\) are related as, in case (a) and case (b), respectively:

1. \(W_P=W_Q;~W_P>W_Q\)
2. \(W_P=W_Q;~W_P=W_Q\)
3. \(W_P>W_Q;~W_P<W_Q\)
4. \(W_P<W_Q;~W_P<W_Q\)
Subtopic:  Elastic Potential Energy |
 73%
From NCERT
NEET - 2015
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A particle of mass \(m\) is driven by a machine that delivers a constant power of \(k\) watts. If the particle starts from rest, the force on the particle at time \(t\) is:
1. \( \sqrt{\frac{m k}{2}} t^{-1 / 2} \)
2. \( \sqrt{m k} t^{-1 / 2} \)
3. \( \sqrt{2 m k} t^{-1 / 2} \)
4. \( \frac{1}{2} \sqrt{m k} t^{-1 / 2}\)

Subtopic:  Power |
 53%
From NCERT
NEET - 2015
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Two particles of masses \(m_1\) and \(m_2\) move with initial velocities \(u_1\) and \(u_2\) respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy \(E\). If the final velocities of particles are \(v_1\) and \(v_2\), then we must have:

1. \(m_1^2u_1+m_2^2u_2-E = m_1^2v_1+m_2^2v_2\)
2. \(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2= \frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\)
3. \(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2-E= \frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\)
4. \(\frac{1}{2}m_1^2u_1^2+\frac{1}{2}m_2^2u_2^2+E = \frac{1}{2}m_1^2v_1^2+\frac{1}{2}m_2^2v_2^2\)
Subtopic:  Collisions |
 62%
From NCERT
NEET - 2015
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A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2\) kg. Hence the particle is displaced from position \((2 \hat{i} + \hat{k})\) meter to position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) meter. The work done by the force on the particle is:

1. \(6\) J 2. \(13\) J
3. \(15\) J 4. \(9\) J

Subtopic:  Concept of Work |
 80%
From NCERT
AIPMT - 2013
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The potential energy of a system increases if work is done:

 
1. by the system against a conservative force
2. by the system against a non-conservative force
3. upon the system by a conservative force
4. upon the system by a non-conservative force

Subtopic:  Potential Energy: Relation with Force |
 67%
From NCERT
AIPMT - 2011
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Force \(F\) on a particle moving in a straight line varies with distance \(d\) as shown in the figure. The work done on the particle during its displacement of \(12\) m is: 

              

1. \(21\) J
2. \(26\) J
3. \(13\) J
4. \(18\) J

Subtopic:  Work Done by Variable Force |
 72%
From NCERT
AIPMT - 2011
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A body of mass \(1\) kg is thrown upwards with a velocity \(20\) ms-1. It momentarily comes to rest after attaining a height of \(18\) m. How much energy is lost due to air friction?
(Take \(g=10\) ms-2)
1. \(20\) J
2. \(30\) J
3. \(40\) J
4. \(10\) J

Subtopic:  Work Energy Theorem |
 87%
From NCERT
AIPMT - 2009
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An engine pumps water continuously through a hose. Water leaves the hose with a velocity \(v\) and \(m\) is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
1. \(\frac{1}{2}mv^3\)
2. \(mv^3\)
3. \(\frac{1}{2}mv^2\)
4. \(\frac{1}{2}m^2v^2\)

Subtopic:  Power |
 78%
From NCERT
AIPMT - 2009
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