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

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

An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60% . If g = 10 ms^–2, the power of the engine is

(1) 3.3 kW

(2) 0.33 kW

(3) 0.033 kW

(4) 33 kW

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) $\frac{1}{2}A\rho v^3$

(2) $\frac{1}{2}A\rho v^2$

(3) $\frac{1}{2}A\rho v$

(4) $A\rho v$

A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is the acceleration due to gravity, the work required to pull the hanging part on the table is:
1. \(MgL\)

2. \(\dfrac{MgL}{3}\)

3. \(\dfrac{MgL}{9}\)

4. \(\dfrac{MgL}{18}\)

If W₁, W₂ and W₃ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W₁, W₂ and W₃ 

(1) W₁ > W₂ > W₃

(2) W₁ = W₂ = W₃

(3) W₁ < W₂ < W₃

(4) W₂ > W₁ > W₃

The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation $t=\sqrt{x}+3$, where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is 

(1) 9 J

(2) 6 J

(3) 0 J

(4) 3 J

A force \(F = -k(y\hat i +x\hat j)\) (where \(k\) is a positive constant) acts on a particle moving in the \(xy\text-\)plane. Starting from the origin, the particle is taken along the positive \(x\text-\)axis to the point \((a,0)\) and then parallel to the \(y\text-\)axis to the point \((a,a)\). The total work done by the force on the particle is:
1. \(-2ka^2\)
2. \(2ka^2\)
3. \(-ka^2\)
4. \(ka^2\)