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Q.
Two masses of $8 kg$ and $4 kg$ are connected by a string as shown in figure over a frictionless pulley. The acceleration of the system is
Laws of Motion
Solution:
$m _{2} g - T = m _{2} a \dots$(1)
$T - m _{1} g \sin 60^{\circ}= m _{1} a \dots$(2)
Adding both equation
$m _{2} g - m _{1} g \sin 60^{\circ}= m _{2} a + m _{1} a$
$\frac{ g \left( m _{2}- m _{1} \sin 60^{\circ}\right)}{\left( m _{2}+ m _{1}\right)}= a$
$\frac{9.8\left(4-8 \times \frac{\sqrt{3}}{2}\right)}{(8+4)}= a$
$a =\frac{9.8 \times(-2.84)}{12}=-2.31 m / s ^{2} $
-Ve sign indicates acceleration is against of gravity.
