Question

Assuming pulley and string to be ideal and masses to be rigid, calculate the common acceleration of the blocks on smooth surface as shown.

• A. $\frac{5-3\sqrt{2}}{16}g$
• B. $\frac{5-\sqrt{3}}{16}g$
• C. $\frac{5+3\sqrt{2}}{16}g$
• D. $\frac{5+\sqrt{3}}{16}g$

Answer 1

The correct option is A $\frac{5-3\sqrt{2}}{16}g$

Here we have two forces $5g\sin {30}^{\circ }=25\text{N}$
and $3g\sin {45}^{\circ }=21.21\text{N}$,
$\because 5g\sin {30}^{\circ }>3g\sin {45}^{\circ }$
blocks are moving towards the right.
$\therefore T-3g\sin {45}^{\circ }=3a$ ----(I)
& $5g\sin {30}^{\circ }-T=5a$ ----(II)
solving (I)&(II), $a=\frac{5-3\sqrt{2}}{16}g$