Question

Two blocks of mass 10 kg and 20 kg are connected by a light string as shown in the figure. If two forces of 50 N and 20 N are exerted on the system, the net acceleration of 10 kg mass will be

• A. $1m/s^2$
• B. $2m/s^2$
• C. $0.5m/s^2$
• D. $3m/s^2$

Answer 1

The correct option is A $1m/s^2$

Let the tension in the string be T and acceleration of both the blocks be a.

Mass of one block, $m_1=10kg$
Mass of the other block, $m_2=20kg$
For block of mass $m_1:$
According to Newton’s second law, $T–20=m_{1}a$
$\Rightarrow T–20=10a\dots ..\left(i\right)$
For block of mass $m_2:$

According to Newton’s second law, $50–T=m_{2}a$

$\Rightarrow 50–T=20a\dots ..\left(ii\right)$
Adding (i) and (ii), we get:
30a = 30
$\Rightarrow a=1m/s^2$
Thus, acceleration of the block of mass 10 kg is 1 $m/s^2$. Hence, the correct answer is option (1).