Question

Two blocks are connected by a cord passing over a small frictionless pulley and resting on frictionless planes as shown in the figure. The acceleration of the blocks is:

• A. $0.33m/s^2$
• B. $0.66m/s^2$
• C. $1m/s^2$
• D. $1.33m/s^2$

Answer 1

The correct option is D $1.33m/s^2$

Let Tension in the string is $T$ and acceleration of the system is $a$
$100g\sin {37}^o-T=100a...\left(1\right)$
$T-50g\sin {53}^o=50a...\left(2\right)$
$\because \sin {53}^o=4/5,\sin {37}^o=3/5$
$60g-T=100a...\left(3\right)$
and $T-40g=50a...\left(4\right)$
from equation (3) and (4)
$20g=150a\Rightarrow a=\frac{2g}{15}=1.33m/s^2$