Question

Two books of masses of 40 kg and 30 kg are connected by a weightless string over a frictionless pulley as shown in the figure.
The acceleration of the system would be:

• A. $0.7m{s}^{-2}$
• B. $0.8m{s}^{-2}$
• C. $0.18m{s}^{-2}$
• D. $0.5m{s}^{-2}$

Answer 1

The correct option is A $0.7m{s}^{-2}$

Here, $m_1=40kg{m}_2=30kg,\theta ={30}^0$

Let T be the tension in the string and a be the acceleration of the system. Their equations of motion are $m_{1}gsin{30}^0-T=m_{1}a$ .............(i)

$T-m_{2}gsin{30}^0=m_{2}a$ ..............(ii)

Adding (i) and (ii), we get

$(m_1+m_2)a=(m_1-m_2)gsin{30}^0$

Substituting the given values, we get

$(40+30)a=(40-30)\times 9.8\times \frac{1}{2}=49$

$a=\frac{49}{70}=0.7m{s}^{-2}$