Question

Find the work done by tension (in $\text{J}$) on $1\text{kg}$ block when $4\text{kg}$ block moves down by $20\text{cm}$ after the system is released. All surfaces are frictionsless

• A. $4\text{J}$
• B. $6\text{J}$
• C. $5\text{J}$
• D. Zero

Answer 1

The correct option is C $5\text{J}$

By the FBD of both the blocks, given that the block $4\text{kg}$ moves down by $0.2\text{m}$ so the block $1\text{kg}$ will move up the incline plane by $0.4\text{m}$


The acceleration of the block $4\text{kg}$ will be $a$ downward and the acceleration of block $1\text{kg}$ will be $2a$ up the incline plane

$\therefore$ From both FBD, we get

$40-2T=4a..\left(i\right)$

$T-1\times 10\times \sin {30}^{\circ }=1.\left(2a\right)..\left(ii\right)$

From $\left(i\right)$ & $\left(ii\right)$, we get
$T=12.5\text{N}$

$\therefore$ Work done due to tension $=T\times 0.4$
on $1\text{kg}$ block $=12.5\times 0.4$
$W_T=5\text{J}$

Hence option C is the correct answer