Five persons \(A,\ B,\ C,\ D\ \text{and}\ E \) are pulling a cart of mass \(100\ \text{kg}\) on a smooth surface, and the cart is moving with an acceleration \(3 \ \text{m /s} ^ 2\) in the East direction. When person \(A\) stops pulling, it moves with an acceleration \(1 \ \text{m /s}^ 2\) in the west direction. When person\(​​B\) stops pulling, it moves with an acceleration \(24 \ \text{m/s}^ 2\) in the north direction. The magnitude of the acceleration of the cart when only \(A\) and\(​​B\) pull the cart, keeping their directions the same as the old directions, is:

1. \(26 \ \text{m/s}^ 2\)
2. \(3\sqrt{71} \ \text{m/s}^ 2\) $\mathrm{}$
3. \(25 \ \text{m/s}^ 2\)
4. \(30 \ \text{m/s}^ 2\)

Two masses, \(m\) and \(M\), are connected by a light string passing over a smooth pulley. When mass \(m\) moves up by \(1.4\) m in \(2\) sec, the ratio \(\frac{m}{M}\) ​​​​is:

The engine of a car produces an acceleration of 4 m/s² in the car. If this car pulls another car of the same mass, what will be the acceleration produced?

1. 8 m/s²

2. 2 m/s²

3. 4 m/s²

4. $\frac{1}{2}m/s^2$   

A truck and a car are moving with equal velocity. If equal retarding force is applied on each, then on applying the brakes both will stop after certain distance 

1. Truck will cover less distance before rest

2. Car will cover less distance before rest

3. Both will cover equal distance

4. None

A constant force acts on a body of mass \(0.9\ \text{kg}\) at rest for \(10\ \text{s}\). If the body moves a distance of \(250\ \text{m}\), the magnitude of the force is:

1. \(3\ \text{N}\)

2. \(3.5\ \text{N}\)

3. \(4.0\ \text{N}\)

4. \(4.5\ \text{N}\)

A body of \(5\ \text{kg}\) is moving with a velocity of \(20\ \text{m/s}\). If a force of \(100\ \text{N}\) is applied to it for \(10\ \text{s}\) in the same direction as its velocity, what will now be the velocity of the body?

1. \(200\ \text{m/s}\)

2. \(220\ \text{m/s}\)

3. \(240\ \text{m/s}\)

4. \(260\ \text{m/s}\)

A cyclist turns around a curve at \(15\ \text{miles/hour}\). If he turns at double the speed, the tendency to overturn is:

1. Doubled
2. Quadrupled
3. Halved
4. Unchanged

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be:
1. \(mg+\dfrac{mv^2}{r}\)
2. \(mg-\dfrac{mv^2}{r}\)
3. \(\dfrac{mv^2g}{r}\)
4. \(\dfrac{v^2g}{r}\)

A motorcyclist moving with a velocity of \(72\ \text{km/h}\) on a flat road takes a turn on the road at a point where the radius of curvature of the road is \(20\ \text{m}\). The acceleration due to gravity is \(10\ \text{m/s}^2\). To avoid skidding, he must not bend with respect to the vertical plane by an angle greater than:

1. \(𝜃=\tan^{−1}6\)

2. \(𝜃=\tan^{−1}2\)$\mathrm{}$

3. \(𝜃=\tan^{−1}25.92\)$$

4. \(𝜃=\tan^{−1}4\)$$

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance \(r\). The speed of the particle is:

1. Proportional to \(r^2\)

2. Independent of \(r\)

3. Proportional to \(r\)

4. Proportional to \(\dfrac 1r\)