A ball is thrown vertically downward from a height of $$20$$ m with an initial velocity $$v_0$$. It collides with the ground, loses $$50\%$$ of its energy in a collision, and rebounds to the same height. The initial velocity $$v_0$$ is:
(Take, $$g=10~\mathrm{ms^{-2}}$$)
1. $$14$$ ms–1
2. $$20$$ ms–1
3. $$28$$ ms–1
4. $$10$$ ms–1

Subtopic:  Gravitational Potential Energy |
64%
From NCERT
NEET - 2015
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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 Subtopic: Elastic Potential Energy | 73% From NCERT NEET - 2015 To view explanation, please take trial in the course. NEET 2023 - Target Batch - Aryan Raj Singh Hints Links To view explanation, please take trial in the course. NEET 2023 - Target Batch - Aryan Raj Singh A block of mass \(10$$ kg, moving in the x-direction with a constant speed of $$10$$ ms–1 is subjected to a retarding force $$F=0.1x$$ J/m during its travel from $$x = 20$$ m to $$30$$ m. Its final kinetic energy will be:
1. $$475$$ J
2. $$450$$ J
3. $$275$$ J
4. $$250$$ J
Subtopic:  Work Energy Theorem |
72%
From NCERT
NEET - 2015
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A particle of mass $$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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On a frictionless surface, a block of mass $$M$$ moving at speed $$v$$ collides elastically with another block of the same mass $$M$$ which is initially at rest. After the collision, the first block moves at an angle $$\theta$$ to its initial direction and has a speed $$\frac{v}{3}$$. The second block’s speed after the collision will be:
1. $$\frac{2\sqrt{2}}{3}v$$
2. $$\frac{3}{4}v$$
3. $$\frac{3}{\sqrt{2}}v$$
4. $$\frac{\sqrt{3}}{2}v$$

Subtopic:  Collisions |
66%
From NCERT
NEET - 2015
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A body of mass ($$4m$$) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass ($$m$$) move perpendicular to each other with equal speeds ($$u$$). The total kinetic energy generated due to explosion is:

 1 $$mu^2$$ 2 $$1.5~mu^2$$ 3 $$2~mu^2$$ 4 $$3~mu^2$$

Subtopic:  Concept of Work |
61%
From NCERT
AIPMT - 2014
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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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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $$1$$ kg moves with a speed of $$12$$ ms–1 and the second part of mass $$2$$ kg moves with $$8$$ ms–1 speed. If the third part flies off with $$4$$ ms–1 speed, then its mass is:
1. $$5$$ kg
2. $$7$$ kg
3. $$17$$ kg
4. $$3$$ kg
Subtopic:  Collisions |
69%
From NCERT
AIPMT - 2013
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A particle with total energy $$E$$ is moving in a potential energy region $$U(x).$$ The motion of the particle is restricted to the region where:
1. $$U(x)<E$$
2. $$U(x)=0$$
3. $$U(x)\leq E$$
4. $$U(x)> E$$
Subtopic:  Conservation of Mechanical Energy |
From NCERT
NEET - 2013