Question

A particle of mass m is projected with velocity u at an angle θ with horizontal. During the period when the particle descends from highest point to the position where its velocity vector makes an angle θ/2 with horizontal. Work done by the gravity force is

• A. $\frac { 1 } { 2 }$mu² tan²θ/2
• B. $\frac { 1 } { 2 }$mu² tan²θ
• C. $\frac { 1 } { 2 }$mu² cos²θ tan²θ/2
• D. $\frac { 1 } { 2 }$mu² cos²θ/2 sin²θ

Answer 1

Answer: (C)

$\frac { 1 } { 2 }$mu² cos²θ tan²θ/2

Answer 2

As horizontal component of velocity does not change, v cos θ/2 = u cos θ, v = $\frac { 1 } { 2 }$mv² − $\frac { 1 } { 2 }$m(ucos θ)² = $\frac { 1 } { 2 }$mu² cos² θ tan²θ/2 Hence, the correct choice is