Question

A ball of mass m is released from A inside a smooth wedge of mass m as shown in the figure. What is the speed of the wedge when the ball reaches point B?

• A. $\left( \frac { \mathrm { gR } } { 3 \sqrt { 2 } } \right) ^ { 1 / 2 }$
• B. $\sqrt { 2 \mathrm { gR } }$
• C. $\left( \frac { 5 \mathrm { gR } } { 2 \sqrt { 3 } } \right) ^ { 1 / 2 }$
• D. $\sqrt { \frac { 3 } { 2 } \mathrm { gR } }$

Answer 1

Answer: (A)

$\left( \frac { \mathrm { gR } } { 3 \sqrt { 2 } } \right) ^ { 1 / 2 }$

Answer 2

0 = $\frac { 1 } { 2 } \mathrm { mv } _ { \mathrm { rel } } ^ { 2 }$ + $\frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$ – mgRcos45⁰

0 = 1/2 m (v²+u² – 2uvcos 45⁰) + 1/2 mv² – mgRcos45⁰.... (1)

p_i = p_f ̃ = – mv+ m(ucos45⁰ – v) ….(2)