Question

A $1kg$ block 'B' rests as shown on a bracket 'A' of same mass. Constant forces $F_1=20N$ and $F_2=8N$ start to act at time $t=0$ when the distance of block B from pulley is $50cm$. Time when block B reaches the pulley is :

• A. $0.5sec$
• B. $1sec$
• C. $2.5sec$
• D. $1.5sec$

Answer 1

The correct option is A $0.5sec$

Block A
Using $F=ma$
$20-16=1\times a1$
or $a1=4m/s^2$

Block B
$8=1\times a2$
or $a2=8m/s^2$
Relative acceleration of block B wrt. A $=4m/s^2$ to the right.
Using eq. $s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 0.5=\frac{1}{2}\times 4t^2$
$\Rightarrow t^2=0.25$
$\Rightarrow t=0.5seconds$
Thus A is the correct answer.