Question

A block of mass m resting on a wedge of angle Ѳ as shown in figure. The wedge is given an
acceleration a. What is the minimum value of a so
that the mass m falls freely?
(A) g
(B) g cos Ѳ
(C) g cot Ѳ
(D) g tan Ѳ ​

Answer 1

Figure

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Acceleration=g\:cot\:\theta}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Mass \: of \: block = m \\ \\ \tt: \implies Angle \: of \: wedge = \theta \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Minimum \: acceleration \: so \: that \: mass \:( m) \:falls \: freely = ?$

• According to given question :

$\bold{As \: according \: to \: given \: fbd} \\ \tt: \implies N \: cos \: \theta = ma - - - - - (1) \\ \\ \tt: \implies N \:sin \: \theta = mg - - - - - (2) \\ \\ \text{Dividing \: (2) \: by \: (1)} \\ \tt: \implies \frac{N \: sin \: \theta}{N \: cos \: \theta} = \frac{mg}{ma} \\ \\ \tt: \implies tan \: \theta = \frac{g}{a} \\ \\ \tt: \implies a = \frac{g}{tan \: \theta} \\ \\ \tt: \implies a = \frac{g}{ \frac{1}{cot \: \theta} } \\ \\ \green{ \tt: \implies a = g \: cot \: \theta} \\ \\ \green{\tt{\therefore Minimum \: acceleration \: is \:( g \: cot \: \theta)}}$