Question

As shown in fig. a $5kg$ mass slips over a plane inclined ${30}^o$ with horizontal. What will be its acceleration when it moves upwards. Other mass is $10kg$. Assume that there is no friction anywhere. $(g=10m/se{c}^2)$

• A. $0.33m/se{c}^2$
• B. $3.3m/se{c}^2$
• C. $33m/se{c}^2$
• D. none of these

Answer 1

The correct option is B $3.3m/se{c}^2$

Since the pulleys are assumed to be massless, so forces on the movable pulley balance-

$2T=T^{{}^{\prime }}$.

Also,$T\ast a$ is constant

So $a^{{}^{\prime }}$ comes out to be $\frac{a}{2}$.($a$ is acceleration of $5kg$ block,and $a^{{}^{\prime }}$ is acceleration of $10kg$ block)

Equation of motion for the $5kg$ block and $10kg$ block are as follows-

$T-5gsin{30}^o=5a$

$10g-2T=10\frac{a}{2}$

From these equations,$a$ comes out to be $\frac{g}{3}m{s}^{-2}$

$a=3.3m{sec}^{-2}$