Question

Find the acceleration of block of mass ${}^{\prime }4m^{\prime }$, assuming that the surface and pulley are smooth and the string is inextensible.

• A. $\frac{6g}{17}$
• B. $\frac{3g}{17}$
• C. $\frac{2g}{17}$
• D. $\frac{g}{17}$

Answer 1

The correct option is A $\frac{6g}{17}$

Let the acceleration of mass $4m$ and $m$ be $a_1$ and $a_2$ respectively.

Using constraint relation,
$\Rightarrow a_1-a_2-a_2=0\Rightarrow a_1=2a_2$ ... (1)
From FBD of ${}^{\prime }4m^{\prime }$ and ${}^{\prime }{m}^{\prime }$, we get
$4mg\sin 30°-T_1=4m{a}_1$ ... (2)
$2T_1-mg=m{a}_2$ ... (3)
Hence
$4mg-2T_1=8m{a}_1$
$2T_1-mg=m\left(\frac{a_1}{2}\right)$
Solving the above two equations, we get
$3mg=m{a}_1\left(\frac{17}{2}\right)$
$\Rightarrow a_1=\frac{6g}{17}$