The relation between velocity (v) and time (t) is $\mathrm{v\alpha }\sqrt{\mathrm{t}}$, then which one of the following quantity is constant:

1.  Force

2.  Power

3.  Momentum

4.  Kinetic Energy

Concept Questions :-

Power
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A particle is moving on the circular path of the radius (R) with centripetal acceleration ${a}_{c}={k}^{2}R{t}^{2}$. Then the correct relation showing power (P) delivered by net force versus time (t) is

1. 1

2. 2

3. 3

4. 4

Concept Questions :-

Power
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A steel wire can withstand a load up to 2940 N. A load of 150 kg is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is (2008 E)

(1) 30$°$

(2) 60$°$

(3) 80$°$

(4) 85$°$

Concept Questions :-

Work-Energy theorem
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A body is thrown vertically up with certain initial velocity, the potential and kinetic energies of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of potential and kinetic energies of the body when it crosses the same point, is

1. 1:1

2. 1:4

3. 1:7

4. 1:8

Concept Questions :-

Gravitational Potential energy
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A body is displaced from (0,0) to (1m,1m) along the path x=y by a force $F=\left({x}^{2}\stackrel{^}{j}+y\stackrel{^}{i}\right)N$. The work done by this force will be :

1. $\frac{4}{3}J$

2. $\frac{5}{6}J$

3. $\frac{3}{2}J$

4. $\frac{7}{5}J$

Concept Questions :-

Work done by variable force
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In the figure shown, the potential energy U of a particle is plotted against its position 'x' from the origin. Then which of the following statement is correct?

1. ${\mathrm{x}}_{1}$ is in stable equilibrium

2. ${\mathrm{x}}_{2}$ is in stable equilibrium

3. ${\mathrm{x}}_{3}$ is in stable equilibrium

4. none of these

Concept Questions :-

Potential energy: Relation with force
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A weightless rod of length 2l carries two equal mass 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in a vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in the horizontal position. The speed of the mass B at the instant rod, become vertical is:

(1) $\sqrt{\frac{3gl}{5}}$

(2) $\sqrt{\frac{4gl}{5}}$

(3) $\sqrt{\frac{6gl}{5}}$

(4) $\sqrt{\frac{7gl}{5}}$

Concept Questions :-

Work-Energy theorem
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A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be

1.  ${\mathrm{Fv}}^{2}$

2.  Fv

3.  $\mathrm{F}/{\mathrm{v}}^{2}$

4.  F/v

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Potential energy (U) related to coordinates is given by U = 3(x + y). Work was done when the particle is going from (0, 0), (2, 3) is:

1.  15 J

2.  -15 J

3.  12 J

4.  10 J

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

1.  0.5 m

2.  0.15 m

3.  0.12 m

4.  1.5 m