Sum

Consider the situation shown in the following figure All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.

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#### Solution

Mass of each block is 1 kg, \[\sin \theta_1 = \frac{4}{5}\]

\[\sin \theta_2 = \frac{3}{5}\]

The free-body diagrams for both the boxes are shown below:

mgsinθ_{1} − T = ma ...(i)

T − mgsinθ_{2} = ma ...(ii)

Adding equations (i) and (ii),we get:

mg(sinθ_{1} − sinθ_{2}) = 2ma

⇒ 2a = g (sinθ_{1} − sinθ_{2})

\[\Rightarrow a = \frac{g}{5} \times \frac{1}{2}\]

\[ = \frac{g}{10}\]

Concept: Newton’s Second Law of Motion

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