Q. No.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. | \(\sqrt{\mu_{s} {Rg}}\) |
A particle of mass \(m\) is suspended from a ceiling through a massless string. The particle moves in a horizontal circle as shown in the given figure. The tension in the string is:
1. \(mg\)
2. \(2mg\)
3. \(3mg\)
4. \(4mg\)
A small coin is kept at a distance \(r\) from the centre of a gramophone disc rotating at an angular speed \(\omega\). The minimum coefficient of friction for which a coin will not slip is:
1. \(\frac{rω^{2}}{g}\)
2. \(\frac{g}{r\omega^2}\)
3. \(\frac{r^2ω^{2}}{g}\)
4. \(\frac{rω}{g}\)
| 1. | \(36\) km/h | 2. | \(54\) km/h |
| 3. | \(72\) km/h | 4. | \(90\) km/h |
A \(10\) kg block is kept on a horizontal turntable that rotates at an angular velocity of \(2\) rad/s. If the distance of the block from the center of the table is \(0.5\) m, the net force on the block is:
1. \(40\) N
2. \(20\) N
3. \(10\) N
4. zero
A massless string of length \(1\) m fixed at one end carries a mass of \(2\) kg at the other end. The string makes \(\frac{2}{\pi}\) rev/s around the axis through the fixed end as shown in the figure. The tension on the string will be:
| 1. | \(32\) N | 2. | \(3\) N |
| 3. | \(16\) N | 4. | \(4\) N |
A ball of mass \(0.1~\text{kg}\) is whirled in a horizontal circle of radius \(1\) m by means of a string at an initial speed of \(10~\text{rpm}\) . Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:
| 1. | \(5~\text{rpm}\) | 2. | \(10~\text{rpm}\) |
| 3. | \(20~\text{rpm}\) | 4. | \(14~\text{rpm}\) |
A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is \(20\) m. The speed of the car at the top of the hill is between:
1. \(14~\text{m/s}~\text{and}~15~\text{m/s}\)
2. \(15~\text{m/s}~\text{and}~16~\text{m/s}\)
3. \(16~\text{m/s}~\text{and}~17~\text{m/s}\)
4. \(13~\text{m/s}~\text{and}~14~\text{m/s}\)
Two masses, \(M\) and \(m\), are attached to a vertical axis by weightless threads of combined length \(l\). They are set in rotational motion in a horizontal plane about this axis with constant angular velocity \(\omega\). If the tensions in the threads are the same during motion, the distance of \(M\) from the axis is:
1. \(\frac{M l}{M + m}\)
2. \(\frac{m l}{M + m}\)
3. \(\frac{M+m}{M}l\)
4. \(\frac{M+m}{m}l\)
A coin placed on a rotating table just slips if it is placed at a distance \(4r\) from the center. On doubling the angular velocity of the table, the coin will just slip when the distance from the centre is equal to:
1. \(4r\)
2. \(2r\)
3. \(r\)
4. \(\frac{r}{4}\)
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