Question

Block $A$ of mass $m$ placed on a smooth inclined plane is connected by a string to another block $B$ of mass $M$ as shown in the figure. If the system is in equilibrium , express $M$ in terms of $m$

• A. $m\sin \theta$
• B. $m\cos \theta$
• C. $2m\sin \theta$
• D. $2m\cos \theta$

Answer 1

The correct option is A $m\sin \theta$

For equilibrium of the block $A$, net force on it must be zero
$N$; Normal reaction from slope

$\sum f_x=0\Rightarrow T=mg\sin \theta ....\left(i\right)$
$\sum f_y=0\Rightarrow N=mg\cos \theta$

For equilibrium of block $B$ the net force on it must be zero.
$\sum F_y=0\Rightarrow T=Mg....\left(ii\right)$

From equation (i) and (ii) , we have $M=m\sin \theta$