A train is moving on a horizontal track. A pendulum suspended from the roof makes an angle of \(4^{o}\) with the vertical. If, \(g=9.8m.s^{-2}\), what is the acceleration of the train?
Ans: \(a=0.7\frac{m}{s^{2}}\).
A mass of \(6kg\) suspended by a rope of length \(2m\) from the celling of a room as shown in figure. A force of \(50N\) is applied at the mid point P of the rope. What is the angle that the rope makes with the vertical in equilibrium? Take: \(g=10m.s^{-2}\) and neglect the mass of the rope.
A body of mass m is suspended by two rope making an angle of \(\alpha\) and \(\beta\) with the horizontal as shown in below figure. Find the tension in the strings.
Ans: \(T_{1}=\frac{mgCos\beta}{Sin\left(\alpha+\beta\right)}\) and \(T_{2}=\frac{mgCos\alpha}{Sin\left(\alpha+\beta\right)}\).
A mass of \(4kg\) is suspended by a rope of length \(4m\) from the celling. A force of \(20N\) in the horizontal direction is applied at the middle point of the rope. What is the angle which rope makes with the vertical direction in the equilibrium? Neglect the mass of the rope. Take: \(g=10m.s^{-2}\).
Ans: \(\theta=tan^{-1}\left(\frac{1}{2}\right)\).
A ball of mass \(2kg\) hangs in equilibrium from two strings OA and OB as show in figure. What are the tension in the string OA and OB?
Ans: \(T_{1}=10N\) and \(T_{2}=10\sqrt{3}N\).
A body of weight \(20N\) is suspended with the help of strings as shown in below figure; What is the magnitude of \(T_{1}\) and \(T_{2}\)?
Ans: \(T_{1}=146.4N\) and \(T_{2}=179.3N\).
A uniform rope of length l, resting on a frictionless horizontal table is rolled at one end by the force F. What is the tension in the rope at a distance \(l^{‘}\) from the end where the force is applied?
