Question

Two masses of $8kg$ and $4kg$ are connected by a string as shown in figure over a frictionless pulley. The acceleration of the system is

• A. $0.1m/s^2$
• B. $4m/s^2$
• C. $3m/s^2$
• D. $2.31m/s^2$

Answer 1

Answer: (D)

$m_{2}g-T=m_{2}a\dots$(1)
$T-m_{1}g\sin 60^{\circ }=m_{1}a\dots$(2)
Adding both equation
$m_{2}g-m_{1}g\sin 60^{\circ }=m_{2}a+m_{1}a$
$\frac{g\left(m_2-m_1\sin 60^{\circ }\right)}{\left(m_2+m_1\right)}=a$

$\frac{9.8\left(4-8\times \frac{\sqrt{3}}{2}\right)}{(8+4)}=a$
$a=\frac{9.8\times (-2.84)}{12}=-2.31m/s^2$
-Ve sign indicates acceleration is against of gravity.