question_answer

A body of mass 0.5 kg is projected under gravity with a speed of 98 m/s at an angle of \[30{}^\circ \] with the horizontal. The magnitude of its change in momentum is

A)  24.5 N-s                     

B)  49.0 N-s         

C)      98.0 N-s          

D)     50.0 N-s                      

Correct Answer: B

Solution :

From figure, it is obvious that only the vertical component of the velocity of projectile is hanging Change in velocity in vertical direction \[=-u\sin \theta -u\sin \theta =-2u\sin \theta .\] Therefore the change in momentum \[=-2\,mu\,\sin \theta \] \[=-2\times 0.5\times 98\times \sin {{30}^{o}}\] \[=-2\times 0.5\times 98\times \frac{1}{2}=-49\,N-s\] Therefore the magnitude of change in its momentum\[=49\,N-s\] Hence, the correction option is [b].