question_answer

A projectile of mass m is thrown with velocity \[\upsilon \]making an angle of \[{{30}^{o}}\] with vertically. Neglecting air resistance the magnitude of change in momentum between the starting point and at the maximum height is

A)  \[\frac{m\upsilon }{2}\]

B)  \[\frac{\sqrt{3}m\upsilon }{2}\]

C)  \[m\upsilon \]

D)  \[\frac{\sqrt{7}m\upsilon }{2}\]

Correct Answer: B

Solution :

At point O, \[=V\,\cos \theta i+V\sin \theta j\] at point O: \[\therefore \] \[{{V}_{f}}=u\,\cos \theta i=\Delta P\,m({{V}_{f}}-{{V}_{i}})\] \[\Delta P=-m\upsilon \,\sin \theta j\] \[|\Delta P|=m\upsilon \,\sin {{60}^{o}}=\frac{\sqrt{3m\upsilon }}{2}\]