Explanation

(a) [image:5_image277.emf]
Let $T$ be the tension in the string
Let $a$ be acceleration of the system
The equations of motion are
$Ma = Mg\sin{53{^\circ}} - T$ …(i)
And $Ma = T - Mg\sin{37{^\circ}}$ …(ii)
Adding (i) and (ii, we get
$a = \frac{Mg(\sin{53{^\circ} - \sin{37{^\circ})}}}{2M}$
$= g\cos{45{^\circ}}\sin{8{^\circ}}$
$\left\lbrack \because\sin A - \sin B = 2\cos\left( \frac{A + B}{2} \right)\sin\left( \frac{A - B}{2} \right) \right\rbrack$
$= 10 \times \frac{1}{\sqrt{2}} \times 0.139$
$= 0.98\ ms^{- 2} \approx 1\ ms^{- 2}$