# A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2. Both of them have the same momentum, but their kinetic energies are E1 and E2 respectively. If m1 > m2 then:  1.  2. ${\mathrm{E}}_{1}>{\mathrm{E}}_{2}$ 3. ${\mathrm{E}}_{1}={\mathrm{E}}_{2}$ 4. ${\mathrm{E}}_{1}<{\mathrm{E}}_{2}$

Subtopic:  Concept of Work |
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A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant k = 50 N/m. The maximum compression of the spring would be :-

1. 0.12 m

2. 1.5 m

3. 0.5 m

4. 0.15 m

Subtopic:  Elastic Potential Energy |
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If two springs, A and B  are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1.  1 : 2
2.  2 : 1
3.  1 : 1
4.  1 : 4

Subtopic:  Elastic Potential Energy |
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When a spring is subjected to 4N force, its length is a metre and if 5N is applied, its length is b metre. If 9N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

Subtopic:  Elastic Potential Energy |
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A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to:

1. $\frac{3}{2}D$

2. D

3. $\frac{7}{4}D$

4. $\frac{5}{4}D$

Subtopic:  Conservation of Mechanical Energy |
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If a stone is projected vertically upward from the ground at a speed of 10 m/s, then it's: (g = 10 $\mathrm{m}/{\mathrm{s}}^{2}$)

1.  Potential energy will be maximum after 0.5 s

2.  Kinetic energy will be maximum again after 1 s

3.  Kinetic energy = potential energy at a height of 2.5 m from the ground

4.  Potential energy will be minimum after 1 s

Subtopic:  Conservation of Mechanical Energy |
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The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1.  10%

2.  20%

3.  Zero

4.  11.5%

Subtopic:  Concept of Work |
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A rigid body of mass 'm' is moving in a circle of radius 'r' with constant speed 'v'. The force on the body is $\frac{{\mathrm{mv}}^{2}}{\mathrm{r}}$ and is always directed towards the center. The work done by this force in moving the body over half the circumference of the circle will be:

1.  $\frac{{\mathrm{mv}}^{2}}{\mathrm{r\pi }}$

2.  ${\mathrm{mr}}^{2}\mathrm{\pi }$

3.  Zero

4.  $2{\mathrm{mv}}^{2}\mathrm{\pi }$

Subtopic:  Concept of Work |
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A particle of mass 10 kg moves with a velocity of $10\sqrt{x}$ SI units, where x is displacement. The work done by the net force during the displacement of the particle from x = 4 m to x = 9 m is:

1.  1250 J

2.  1000

3.  3500 J

4.  2500 J

Subtopic:  Work Energy Theorem |
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The potential energy of a particle of mass m varies as the magnitude of the $U=a{x}^{2}+by.$ The magnitude of the acceleration of the particle at (0, 3) is: (symbols have their usual meaning)

1.  $\sqrt{\frac{\mathrm{b}}{\mathrm{m}}}$

2.  $\sqrt{\frac{3\mathrm{b}}{\mathrm{m}}}$

3.  $\frac{\mathrm{b}}{\mathrm{m}}$

4.  Zero

Subtopic:  Potential Energy: Relation with Force |
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