Three blocks \(A\), \(B\) and \(C\) of mass \(3M\), \(2M\) and \(M\) respectively are suspended vertically with the help of springs \(\mathrm{PQ}\) and \(\mathrm{TU}\) and a string \(\mathrm{RS}\) as shown in fig. The acceleration of blocks \(A\), \(B\) and \(C\) are \(a_{1} , a_{2}~ \text{and}~ a_{3}\) respectively.
The value of acceleration \(a_{1}\) at the moment string \(\mathrm{RS}\) is cut will be:
1. \(g\) downward
2. \(g\) upward
3. more than \(g\) downward
4. zero
If \(\mu\) between block \(A\) and inclined plane is \(0.5\) and that between block \(B\) and the inclined plane is \(0.8\), then the normal reaction between blocks \(A\) and \(B\) will be:
1. \(180\) N
2. \(216\) N
3. \(0\)
4. None of these
A particle of mass \(m\) having speed \(v\) goes in a vertical circular motion such that its centre is at its origin, as shown in the figure. If at any instant the angle made by the string with a negative \(y\text-\)axis is \(\theta\) then the tension in the string is:
[Take radius = \(R\)]
1. \(mg\sin\theta+ \frac{mv^2}{R}\)
2. \(mg\cos\theta- \frac{mv^2}{R}\)
3. \(mg\cos\theta+ \frac{mv^2}{R}\)
4. \(mg\sin\theta- \frac{mv^2}{R}\)
Calculate the reading of the spring balance shown in the figure: (take \(g=10\) m/s2)
1. \(60\) N
2. \(40\) N
3. \(50\) N
4. \(80\) N
1. |
\(\overrightarrow N+\overrightarrow T+\overrightarrow W=0\) |
2. | \(T^2=N^2+W^2\) |
3. | \(T = N + W\) | 4. | \(N = W \tan \theta\) |
The angle of banking for a cyclist taking a turn at a curve is given by \(\tan\theta = \frac{v^{n}}{rg}\) where symbols have their usual meaning. The value of \(n\) is:
1. | \(1\)
|
2. | \(2\)
|
3. | \(3\)
|
4. | \(4\) |
A body of mass \(m\) is moving on a concave bridge \(ABC\) of the radius of curvature \(R\) at a speed \(v\). The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:
1. \(mg-\frac{mv^{2}}{R}\)
2. \(mg+\frac{mv^{2}}{R}\)
3. \(mg\)
4. \(\frac{mv^{2}}{R}\)
A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then the train is:
1. | moving with constant velocity. |
2. | in accelerated motion. |
3. | in retarded motion. |
4. | at rest. |
The kinetic energy 'K' of a particle moving in a circular path varies with the distance covered S as K = a, where a is constant. The angle between the tangential force and the net force acting on the particle is: (R is the radius of the circular path)
1.
2.
3.
4.
Choose the incorrect alternative:
1. | Newton's first law is the law of inertia. |
2. | Newton's first law states that if the net force on a system is zero, the acceleration of any particle of the system is not zero. |
3. | Action and reaction act simultaneously. |
4. | The area under the force-time graph is equal to the change in momentum. |