Question

As shown in figure, two blocks $A$ and $B$ of mass $1\text{kg}$ each are connected by an ideal string that passes over a smooth pulley that is fixed on a smooth fixed wedge as shown. If the ratio of normal reaction on block $A$ and on block $B$ is $\frac{4}{3}$ then

• A. $\cos \theta =\frac{4}{5}$
• B. $\sin \theta =\frac{4}{5}$
• C. acceleration of blocks is $\frac{g}{10}$
• D. acceleration of blocks is $\frac{g}{5}$

Answer 1

Answer: (A), (C)

The correct options are
A $\cos \theta =\frac{4}{5}$
C acceleration of blocks is $\frac{g}{10}$

Normal force acting on the block $A$ is given by $N_A=mgcos\theta$
Normal force acting on the block $B$ is given by $N_B=mg\cos {53}^{\circ }$
as given $\frac{N_A}{N_B}=\frac{4}{3}\Rightarrow \frac{\cos \theta }{\cos {53}^{\circ }}=\frac{4}{3}$
$\therefore \cos \theta =\frac{4}{3}\times \frac{3}{5}\Rightarrow \cos \theta =\frac{4}{5}$
Now, $a=\frac{mg[\sin {53}^{\circ }-\sin \theta ]}{2m}=\frac{g}{10}$