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 shell initially at rest explodes into two pieces of equal mass, then the two pieces will 

(1) Be at rest

(2) Move with different velocities in different directions

(3) Move with the same velocity in opposite directions

(4) Move with the same velocity in same direction

A cannon ball is fired with a velocity 200 m/sec at an angle of 60° with the horizontal. At the highest point of its flight ,it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity 

(1) 100 m/s in the horizontal direction

(2) 300 m/s in the horizontal direction

(3) 300 m/s in a direction making an angle of 60° with the horizontal

(4) 200 m/s in a direction making an angle of 60° with the horizontal

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be 

(1) 11.5 m/s

(2) 14.0 m/s

(3) 7.0 m/s

(4) 9.89 m/s

A ²³⁸U nucleus decays by emitting an alpha particle of speed v ms^–1. The recoil speed of the residual nucleus is (in ms^–1) 

(1) –4v/234

(2) v/4

(3) –4v/238

(4) 4v/238

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is 

(1) $\frac{2uM}{m}$

(2) $\frac{2um}{M}$

(3) $\frac{2u}{1+\frac{m}{M}}$

(4) $\frac{2u}{1+\frac{M}{m}}$

A particle of mass m moving with horizontal speed 6 m/sec as shown in figure. If m << M then for one dimensional elastic collision, the speed of lighter particle after collision will be 

(1) 2m/sec in original direction

(2) 2 m/sec opposite to the original direction

(3) 4 m/sec opposite to the original direction

(4) 4 m/sec in original direction

A shell of mass m moving with velocity v suddenly breaks into 2 pieces. The part having mass m/4 remains stationary. The velocity of the other shell will be 

(1) v

(2) 2v

(3) $\frac{3}{4}v$

(4) $\frac{4}{3}v$