Question

Consider the situation shown in figure (5-E9). All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

Answer 1

It is clear that the triangle is a right angled triangle and the vertex angle at pulley is 90°. See the diagram below.

Let angle ACB = θ . The component of weight mg along the 3 m side =mg.cosθ  = 4mg/5. The component of weight mg along the 4 m side =mg.sinθ  = 3mg/5.Let tension in the string be T and the acceleration of the blocks along planes be a.  

Consider the forces and acceleration along the plane on left side block,  4mg/5 - T = ma, →T=4mg/5-ma ........... (A)  

 Consider the forces and acceleration along the plane on right side block,      

T-3mg/5 =ma,       

4mg/5-ma-3mg/5=ma,   {Putting the value of T from (A)}     

 → 2ma = mg/5     

→ a=g/10.     

So the acceleration of the blocks is g/10.

Answer 2

That is the magnitude of the acceleration of the two blocks