At a wall, \(N\) bullets, each of mass \(m\), are fired with a velocity \(v\) at the rate of \(n\) bullets/sec upon the wall. The bullets are stopped by the wall. The reaction offered by the wall to the bullets is:
1. \(\frac{Nmv}{n}\)
2. \(nNmv\)
3. \(n\frac{Nv}{m}\)
4. \(nmv\)
A man of mass \(m\) stands on a crate of mass \(M\). He pulls on a light rope, passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the man on the rope will be:
1. | \(mg\) | 2. | \(Mg\) |
3. | \({1 \over 2}(M + m)g\) | 4. | \((m + M)g\) |
In the shown system, each of the blocks is at rest. The value of \(\theta\) is:
1. \(\tan^{- 1} \left(1\right)\)
2. \(\tan^{- 1} \left(\frac{3}{4}\right)\)
3. \(\tan^{- 1} \left(\frac{4}{3}\right)\)
4. \(\tan^{- 1} \left(\frac{3}{5}\right)\)
A block of mass \(1\) kg lying on the floor is subjected to a horizontal force given by, \(F=2\sin\omega t\) newtons. The coefficient of friction between the block and the floor is \(0.25\). The acceleration of the block will be:
1. positive and uniform
2. positive and non–uniform
3. zero
4. depending on the value of \(\omega\).
A block of mass \(10~\text{kg}\) is in contact with the inner wall of a hollow cylindrical drum of radius \(1~\text{m}\). The coefficient of friction between the block and the inner wall of the cylinder is \(0.1\). The minimum angular velocity needed for the cylinder, which is vertical and rotating about its axis, will be: \(\left(g= 10~\text{m/s}^2\right )\)
1. \(10~\pi~\text{rad/s}\)
2. \(\sqrt{10}~\pi~\text{rad/s}\)
3. \(\frac{10}{2\pi}~\text{rad/s}\)
4. \(10~\text{rad/s}\)
A tube of length \( L\) is filled completely with an incompressible liquid of mass \(M\) and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\omega\). The force exerted by the liquid at the other end is:
1. | \(ML \omega^2 \over 2\) | 2. | \(ML^2 \omega \over 2\) |
3. | \(ML \omega^2 \) | 4. | \(ML^2 \omega^2 \over 2\) |
A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time:
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)
A block of mass \(m\) is in contact with the cart \((C)\) as shown in the figure.
The coefficient of static friction between the block and the cart is \(\mu.\) The acceleration \(a\) of the cart that will prevent the block from falling satisfies:
1. \(a > \frac{mg}{\mu}\)
2. \(a > \frac{g}{\mu m}\)
3. \(a \ge \frac{g}{\mu}\)
4. \(a < \frac{g}{\mu}\)
A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:
1. | \(20\) ms–1 | 2. | \(30\) ms–1 |
3. | \(5\) ms–1 | 4. | \(10\) ms–1 |
A body of mass \(5\) kg is suspended by the strings making angles \(60^\circ\)
Then:
(A) | \( {T}_1=25~ \text{N} \) |
(B) | \( {T}_2=25 ~\text{N} \) |
(C) | \({T}_1=25 \sqrt{3}~ \text{N} \) |
(D) | \({T}_2=25 \sqrt{3}~ \text{N} \) |
1. | (A), (B), and (C) only |
2. | (A) and (B) only |
3. | (A) and (D) only |
4. | (A), (B), (C), (D) |