An object of mass, \(5 kg\) placed on an inclined plane (which is at an angle of \(30^{\circ}\) to the horizontal) is attached to a \(10 kg\) mass through a pulley, with the \(10 kg\) hanging vertically. Calculate the acceleration of the mass-system in terms of the acceleration due to gravity, \(g\), if there is no friction between the \(5 kg\) mass and the plane.
A. \(\frac{2}{5} g\) B. \(\frac{3 g }{5}\) C. \(\frac{1}{2} g\) D. \(\frac{3}{2} g\)
Correct Answer: C
Explanation
given: \(m_{1}=5 kg , m_{2}=10 kg , \theta=30^{\circ}\) free body diagram Since \(10 kg >5 kg\) mass, the motion is downward as shown for the \(10 kg\) mass \(mg >T, m _{2} g - T = ma\) \(10 g -T=10 a \cdots\) (1) for the \(5 kg\) mass \(T- mgsin \theta= ma\) \(T-5 g \sin 30=5 a\) \(T-2.5 g =5 a \ldots(2)\) add (1) and (2) \(7.5 g =15 a\) \(a=\frac{7.5 g }{15}=\frac{1}{2} g\)
