Newton’s Laws Of Motion (11Acd07)

Sheet 06 Higher Order Thinking Skills.

1. The pulley and string shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, What should be the angle \(\theta\)?
   
   
   Ans: \(\theta=Cos^{-1}\left(\frac{1}{\sqrt{2}}\right)=45^{o}\).
   
   
2. The pulley arrangement in the figures are identical. The mass of the rope is negligible. In (a), the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force of 2mg. Then in which case acceleration will be more?
   
   
   Ans: \(2^{nd}Case\).
   
   
3. An insect crawls up a hemispherical surface very slowly. The co-efficient of friction between the insect and the surface is \(\frac{1}{3}\). If the line joining the centers of the hemispherical surface to the insect makes an angle \(\alpha\) with the vertical. Fund: the maximum possible value of \(\alpha\).
   
   Ans: \(Cos\alpha=3\).
   
   
4. In terms of masses \(m_{1}\), \(m_{2}\) and \(g\). Find: the acceleration of the both the blocks as shown in figure. Neglect all friction and masses of the pulley and string.
   
   
   Ans: \(a_{1}=\frac{2m_{2}g}{\left(4m_{1}+m_{2}\right)}\) and \(a_{2}=\frac{m_{2}g}{\left(4m_{1}+m_{2}\right)}\).
   
   
5. A disc of mass \(10g\) is kept on floating horizontally by throwing 10 marbles per second against it from below. If, the mass of each marble is \(5g\). Calculate: the velocity with which the marbles are striking the disc. Assume that the marbles strikes the disc normally and rebound downward with same speed.
   
   Ans: \(V_{strike}=1.47\frac{m}{s}\).
   
   
6. A \(10g\) bullet is fired from a gun horizontally into a \(5kg\) block of wood suspended by a string and the bullet gets embedded in the block. The impact causes the block to swing up to a height of \(5cm\) above the initial level. Calculate: the velocity with which bullet strikes the block?
   
   Ans: \(V_{bullet}=496\frac{m}{s}\).
   
   
7. Two blocks of mass \(1kg\) and \(2kg\) are connected by an inextensible string passes over a frictionless pulley as shown below.
   
   Calculate: the acceleration of the blocks.
   
   Ans: \(a=0.437\frac{m}{s}\).
   
   
8. Two identical point masses each of mass M are connected to one another by a massless string of length L. A constant force F is applied at the mid point of the string. If L be the instantaneous distance between the two masses, what will be acceleration of each mass?
   
   Ans: \(a=\frac{F}{2M}\frac{l}{\sqrt{L^{2}-l^{2}}}\)