Question

In the system shown, the initial acceleration of the wedge of mass $5 \,M$ is (there is no friction anywhere):

• A. Zero
• B. $2 g / 23$
• C. $3 g / 23$
• D. None

Answer 1

Answer: (B)

$2 M g-T =2 M a_{1} \,\,\,$...(i)
$ T+M a_{2} =M a_{1} \,\,\,\,$...(2)

$N=2 M a_{2}\,\,\,$...(3)
$T-N=5 M a_{2}\,\,\,$...(4)
$T=7 M a_{2}\,\,\,$...(5)
From (2) &(5), we get
$7 M a_{2}+M a_{2} =M a_{1} $
$8 a_{2} =a_{1} \,\,\,$...(6)
$2 M g-7 M a_{2} =2 M\left(8 a_{2}\right)$
$a_{2} =\frac{2 g}{23}$