A body of mass \(m\) accelerates uniformly from rest to \(v_1\) in time \(t_1\). As a function of time \(t\), the instantaneous power delivered to the body will be:
1. \(\dfrac{mv_1t}{t_1}\)
2. \(\dfrac{mv^2_1t}{t_1}\)
3. \(\dfrac{mv_1t^2}{t_1}\)
4. \(\dfrac{mv^2_1t}{t^2_1}\)

Subtopic:  Power |
 56%
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A 60 kg man runs up a staircase in 12 seconds while a 50 kg man runs up the same staircase in 11, seconds, the ratio of the rate of doing their work is 

(1) 6 : 5

(2) 12 : 11

(3) 11 : 10

(4) 10 : 11

Subtopic:  Power |
 74%
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What average horsepower is developed by an 80 kg man while climbing in 10 s a flight of stairs that rises 6 m vertically 

(1) 0.63 HP

(2) 1.26 HP

(3) 1.8 HP

(4) 2.1 HP

Subtopic:  Power |
 73%
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An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is

(1) 12Aρv3

(2) 12Aρv2

(3) 12Aρv

(4) Aρv

Subtopic:  Power |
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A particle free to move along the x-axis has potential energy given by U(x)=k[1e-x2] for x+, where k is a positive constant of appropriate dimensions. Then 

(1) At point away from the origin, the particle is in unstable equilibrium

(2) For any finite non-zero value of x, there is a force directed away from the origin

(3) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin

(4) For small displacements from x = 0, the motion is simple harmonic

Subtopic:  Potential Energy: Relation with Force |
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The potential energy of a system is represented in the first figure. the force acting on the system will be represented by

(1)

(2)

(3)

(4)

Subtopic:  Potential Energy: Relation with Force |
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The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig.

The body is in stable equilibrium at

(1) x = x1

(2) x = x2

(3) both x1 and x2

(4) neither x1 nor x2

Subtopic:  Potential Energy: Relation with Force |
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The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at

(1) C

(2) B

(3) B and C

(4) A and D

Subtopic:  Potential Energy: Relation with Force |
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A particle is placed at the origin and a force F = kx is acting on it (where k is positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function) 

(1)

(2)

(3)

(4)

Subtopic:  Elastic Potential Energy |
 56%
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Two particles of masses m1,m2 move with initial velocities u1 and u2. On collision, one of the particles get excited to higher level, after absorbing energy ε. If final velocities of particles be v1 and v2, then we must have

(a)m12u1+m22u2-ε=m12v1+m22v2

(b)12m1u12+12m2u2=12m1v12+12m2v22-ε

(c)12m1u12+12m2u22-ε=12m1v12+12m2v22

(d)12m12u12+12m22u22+ε=12m12v12+12m22v22

Subtopic:  Work Energy Theorem |
 63%
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