Question

If block $A$ is moving with an acceleration of $5m/s^2$, the acceleration of $B$ w.r.t. ground is:

• A. $5m/s^2$
• B. $5\sqrt{2}m/s^2$
• C. $5\sqrt{5}m/s^2$
• D. $10m/s^2$

Answer 1

The correct option is C $5\sqrt{5}m/s^2$

R.E.F image

When Block -A is, reference

length of string $l_1+l_2+l_3+l_4$

$l=l_1+l_2+l_3+l_4$

By double differentiation w.r.t t,

we have

$0=a_1+a_2+a_3+a_4$

$\Rightarrow 0=a+0+a+a_4$

$-2a=a_4$

wrt ground

acceleration of Block-B $\overrightarrow{a_4}+\overrightarrow{a}$

$\Rightarrow \overrightarrow{a_B}=\overrightarrow{a_4}+\overrightarrow{a}$

$\Rightarrow a_B=|{\overrightarrow{a}}_4+\overrightarrow{a}|$

$\Rightarrow a_B=\sqrt{a{4}^2+a^2+2a4-a\left(d\right)}$

$\Rightarrow a_B=\sqrt{4a^2+a^2+2a\left(2a\right)co\left({90}^{\circ }\right)}$

$\Rightarrow a_B=\sqrt{5a}$

As $a=5m/s^2$

$a_B=5\sqrt{5}m/s^2$

Option $-C$ is correct