The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1. ${\tan }^{-1}(0.25)$
2. ${\tan }^{-1}(0.55)$
3. ${\tan }^{-1}(0.45)$
4. ${\tan }^{-1}(0.75)$

A body of mass \(5\) kg is suspended by the strings making angles $\mathrm{}$\(60^\circ\) and $\mathrm{}$\(30^\circ\) with the horizontal.

 
Then:

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 \(g=10~\text{m/s}^2)\)

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:
                         

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. \(\dfrac{rω^{2}}{g}\)
2. \(\dfrac{g}{r\omega^2}\)
3. \(\dfrac{r^2ω^{2}}{g}\)
4. \(\dfrac{rω}{g}\)

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. \(a > \dfrac{mg}{\mu}\)
2. \(a > \dfrac{g}{\mu m}\)
3. \(a \ge \dfrac{g}{\mu}\)
4. \(a < \dfrac{g}{\mu}\)

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:

The force \(F\) acting on a particle of mass \(m\) 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. \(24~\text{N-s}\)
2. \(20~\text{N-s}\)
3. \(12~\text{N-s}\)
4. \(6~\text{N-s}\)

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.)