Two masses M_1 and M_2 are arranged as shown | vedclass

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(A) For the given system,the equation of motion is derived from the net force divided by the total mass.$a = \frac{M_2 g \sin 	heta}{M_1 + M_2}$When

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$\left(\frac{M_1+M_2}{4 M_1+M_2}\right) a$

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(A) For the given system,the equation of motion is derived from the net force divided by the total mass.$a = \frac{M_2 g \sin 	heta}{M_1 + M_2}$When the mass of $M_1$ is doubled $(M_1' = 2M_1)$ and the mass of $M_2$ is halved $(M_2' = M_2/2)$,the new acceleration $a'$ is:$a' = \frac{M_2' g \sin 	heta}{M_1' + M_2'} = \frac{(M_2/2) g \sin 	heta}{2M_1 + M_2/2}$Multiplying the numerator and denominator by $2$:$a' = \frac{M_2 g \sin 	heta}{4M_1 + M_2}$Now,express $a'$ in terms of $a$:$a' = \left( \frac{M_2 g \sin 	heta}{M_1 + M_2} ight) 	imes \left( \frac{M_1 + M_2}{4M_1 + M_2} ight) = a \left( \frac{M_1 + M_2}{4M_1 + M_2} ight)$

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