The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1.
2.
3.
4.
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) |
A block \(A\) of mass \(7\) kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body \(B\) of mass \(3\) kg at the other end. The acceleration of the system will be: (given \(g=10~\text{m/s}^2)\)
1. | \(100\) ms–2 | 2. | \(3\) ms–2 |
3. | \(10\) ms–2 | 4. | \(30\) ms–2 |
A plank with a box on it at one end is gradually raised at the other end. As the angle of inclination with the horizontal reaches \(30^{\circ}\), the box starts to slip and slides \(4.0\) m down the plank in \(4.0\) s. The coefficients of static and kinetic friction between the box and the plank, respectively, will be:
1. | \(0.6\) and \(0.6\) | 2. | \(0.6\) and \(0.5\) |
3. | \(0.5\) and \(0.6\) | 4. | \(0.4\) and \(0.3\) |
A man of mass \(60\) kg is standing on the ground and holding a string passing over a system of ideal pulleys. A mass of \(10\) kg is hanging over a light pulley such that the system is in equilibrium. The force exerted by the ground on the man is: (\(g=\) acceleration due to gravity)
1. \(20g\)
2. \(45g\)
3. \(40g\)
4. \(60g\)
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. \(\frac{rω}{g}\)
A block of mass \(\mathrm{m}\) is in contact with the cart C as shown in the figure.
The coefficient of static friction between the block and the cart is . The acceleration of the cart that will prevent the block from falling satisfies:
1.
2.
3.
4.
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 |
The force \(\mathrm{F}\) acting on a particle of mass \(\mathrm{m}\) is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from \(0\) to \(8\) s is:
1. | \(24\) N-s | 2. | \(20\) N-s |
3. | \(12\) N-s | 4. | \(6\) N-s |
A system consists of three masses \(m_1\), \(m_2\), and \(m_3\) connected by a string passing over a pulley \(\mathrm{P}\). The mass \(m_1\) hangs freely, and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction = \(\mu\)). The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is: (Assume \(m_1=m_2=m_3=m\) and \(g\) is the acceleration due to gravity.)
1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \( \frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)