Question

A block of mass m is placed on a wedge of mass m and inclination θ as shown in Fig. All surfaces are smooth. Find the acceleration of wedge.

• A. $\frac { m g \cos ^ { 2 } \theta } { M + m \sin ^ { 2 } \theta }$
• B. $\frac { m g \sin ^ { 2 } \theta } { M + m \cos ^ { 2 } \theta }$
• C. $\frac { m g \sin \theta \cos \theta } { M + m \sin ^ { 2 } \theta }$
• D. $\frac { m g \sin \theta \cos \theta } { M + m \cos ^ { 2 } \theta }$

Answer 1

Answer: (C)

$\frac { m g \sin \theta \cos \theta } { M + m \sin ^ { 2 } \theta }$

Answer 2

ma = mg sin θ + ma₀ sin θ

or a = g sin θ + a₀cosθ … (i)

N = mg cos θ - ma₀ sin θ ….. (ii)

N sin θ = Ma₀ …. (iii)

From (ii) and (iii)

$\frac { \mathrm { Ma } _ { 0 } } { \sin \theta }$ = mg cos θ - ma₀ sin θ

or a₀ = $\frac { m g \cos \theta \sin \theta } { M + m \sin ^ { 2 } \theta }$