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

A body falls on a surface of coefficient of restitution 0.6 from a height of 1 m. Then the body rebounds to a height of 

(1) 0.6 m

(2) 0.4 m

(3) 1 m

(4) 0.36 m

A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is 

(1) $h\left(\frac{{\displaystyle 1+e^2}}{{\displaystyle 1-e^2}}\right)$

(2) $h\left(\frac{{\displaystyle 1-e^2}}{{\displaystyle 1+e^2}}\right)$

(3) $\frac{h}{2}\left(\frac{{\displaystyle 1-e^2}}{{\displaystyle 1+e^2}}\right)$

(4) $\frac{h}{2}\left(\frac{{\displaystyle 1+e^2}}{{\displaystyle 1-e^2}}\right)$

A body of mass 5 kg moving with a velocity 10m/s collides with another body of the mass 20 kg at, rest and comes to rest. The velocity of the second body due to collision is 

(1) 2.5 m/s

(2) 5 m/s

(3) 7.5 m/s

(4) 10 m/s

A ball of mass m moving with velocity V, makes a head on elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive, velocities of the two balls after collision are-

(1) –V and 2V

(2) 2 V and –V

(3) V and –2V

(4) –2V and V

A spacecraft of mass 'M' and moving with velocity 'v' suddenly breaks in two pieces. After the explosion one of the mass 'm' becomes stationary. What is the velocity of the other part of craft 

(1) $\frac{Mv}{M-m}$

(2) v

(3) $\frac{Mv}{m}$

(4) $\frac{M-m}{m}v$