A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represent the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:
1. | \(\sqrt{\mu_{s} mRg} \) | 2. | \(\sqrt{Rg / \mu_{s}}\) |
3. | \(\sqrt{mRg / \mu_{s}} \) | 4. | \(\sqrt{\mu_{s} {Rg}}\) |
One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the centre) will be: (\(T\) represents the tension in the string)
1. | \(T \) | 2. | \(T+\frac{m v^2}{l} \) |
3. | \(T-\frac{m v^2}{l} \) | 4. | \(\text{zero}\) |
Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in the radius \(r\). The tangential speed of lighter stone is \(n\) times that of heavier stone when they experience the same centripetal forces. The value of \(n\) is:
1. | \(2\) | 2. | \(3\) |
3. | \(4\) | 4. | \(1\) |
A block of mass \(m\) lying on a rough horizontal plane is acted upon by a horizontal force \(P\) and another force \(Q\) inclined at an angle \(\theta\) to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is:
1. \(\dfrac{(P+Q\sin\theta)}{(mg+Q\cos\theta)}\)
2. \(\dfrac{(P\cos\theta+Q)}{(mg-Q\sin\theta)}\)
3. \(\dfrac{(P+Q\cos\theta)}{(mg+Q\sin\theta)}\)
4. \(\dfrac{(P\sin\theta-Q)}{(mg-Q\cos\theta)}\)
Block \(\mathrm{A}\) has a mass of \(10\) kg. Between block \(\mathrm{A}\) and the table, the coefficient of static friction is \(0.2\), and the coefficient of kinetic friction is also \(0.2\). The required mass of \(\mathrm{B}\) to start the motion will be:
1. | \(2~\text{kg}\) | 2. | \(2.2~\text{kg}\) |
3. | \(4.8~\text{kg}\) | 4. | \(200~\text{gm}\) |
A uniform chain of length \(L\) hangs partly from a table which is kept in equilibrium by friction. If the maximum length that can be supported without slipping is \(l,\) then the coefficient of friction between the table and the chain is:
1. \(\frac{l}{L}\)
2. \(\frac{l}{L+l}\)
3. \(\frac{l}{L-l}\)
4. \(\frac{L}{L+l}\)
The variation of momentum with the time of one of the bodies in a two-body collision is shown in fig. The instantaneous force is the maximum corresponding to the point:
1. \(P\)
2. \(Q\)
3. \(R\)
4. \(S\)
A block \(B\) is placed on top of block \(A\). The mass of block \(B\) is less than the mass of block \(A\). Friction exists between the blocks, whereas the ground on which block \(A\) is placed is assumed to be smooth. A horizontal force \(F\), increasing linearly with time begins to act on \(B\). The acceleration \(a_A\) and \(a_B\) of blocks \(A\) and \(B\) respectively are plotted against \(t\). The correctly plotted graph is:
1. | 2. | ||
3. | 4. |
A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by:
1. \(\sqrt{2} M g\)
2. \(\sqrt{2} m g\)
3. \(g\sqrt{\left( M + m \right)^{2} + m^{2}}\)
4. \(g\sqrt{\left(M + m \right)^{2} + M^{2}}\)
The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be:
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)