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

A body of mass \(M\) hits normally a rigid wall with velocity \(v\) and bounces back with the same velocity. The impulse experienced by the body is:
1.  \(1.5Mv\)
2. \(2Mv\)
3. zero
4. \(Mv\)

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. \(a < \dfrac{g}{\mu}\)

The mass of a lift is \(2000\) kg. When the tension in the supporting cable is \(28000\) N, then its acceleration is:
(Take \(g=10\) m/s²)

Two blocks of masses \(2\) kg and \(3\) kg are tied at the ends of a light inextensible string passing over a frictionless pulley as shown.

If the system is accelerating upward with acceleration \(5\) m/s², the tension in the string is:
1. \(24\) N
2. \(36\) N
3. \(48\) N
4. \(18\)N

A body, under the action of a force \(\overset{\rightarrow}{F} = 6 \hat{i} - 8 \hat{j} + 10 \hat{k}\), acquires an acceleration of 1 ms^-2. The mass of this body must be:

1. 2 √10 kg

2. 10 kg

3. 20 kg

4. 10 √2 kg

A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time: 
 
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)