Two masses `M_(1)=5kg,M_(2)=10`kg are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When masses are released, then acceleration of masses will be

Options

A. ` g `
B. ` g // 2 `
C. ` g // 3 `
D. ` g// 4 `

Answer

C

Explanation

Since ` M _ 2 gt M _ 1 `, therefore ` M _ 2 ` moves downwards and ` M _ 1 ` moves upwards with an acceleration a as shown in the figure.

Free body diagram of ` M _ 1 `

The equation of motion for ` M _ 1 ` is
` T - M _ 1 g = M _ 1 a " " `... (i)
Free body diagram of ` M _ 2 `

The equation of motion for ` M _ 2 ` is
` M _ 2 g - T = M _ 2 a " " `...(ii)
Adding (i) and (ii) , we get
` a = ((M _ 2 - M _ 1 ) g ) /( M _ 2 + M _ 1 ) = ((10 - 5 ) g ) /( ( 10 + 5 ) ) = ( g ) /( 3 ) `