Question

if a pulley in the diagram are smooth and massless and a1 and a2 are acceleration of blocks of mass 4kg and 8kg respectively then

Answer 1

Final Answer : (b) $a_1 = 2a_2$

Method -1 :
Steps:
1) If the wire joining, 8kg and pulley is displaced 'x' distance in forward direction.
Then, with connecting 4kg and pulley will move '2x'distance in forward direction as wire in lower part is fixed.

=> This similar holds for acceleration as

$a = \frac{ {d}^{2} x}{d {t}^{2} }$

=> $a_1 = 2a_2$

Method - 2
1) Since, wire in lower part is fixed, so it's acceleration is 0.
By Pulley Constraint,
$a _{2} = \frac{a _{1} + 0}{2} \\ = > \boxed{2a _{2} = a _{1}}$

Hence,Option 2 is answer.

Answer 2

Explanation:

See the pics attached(2 pics) for your answer