A fireman slides down a rope whose maximum sustainable tension is \(\dfrac 23\) of his weight. The minimum downward acceleration required to prevent the rope from breaking is:

1. \(\dfrac 23 g\)

2. \(g\)

3. \(\dfrac 13 g\)

4. Zero

A ball of mass \(m\) moving with speed \(v\), strikes a wall normally and rebounds with the same speed. If the contact time is \(t\), the magnitude of the average force exerted by the ball on the wall is:
 
1. \(\dfrac {2mv}{t}\)

2. \(\dfrac {mv}{t}\)

3. \(mvt\)

4. \(\dfrac {mv}{2t}\)

A body of mass \(5\ \text{kg}\) starts from the origin with an initial velocity \(\vec u=30\hat i+40 \hat j\ \text{ms}^{-1}\). If a constant force \(\vec F=-(\hat i+5 \hat j)\ \text{N}\) acts on the body, the time at which the \(y\)–component of the velocity becomes zero is:

1. \(5\) seconds
2. \(20\) seconds
3. \(40\) seconds
4. \(80\) seconds

A ball of mass \(0.5\ \text{kg}\) moving with a velocity of \(2\ \text{m/s}\) strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is one millisecond, the average force exerted by the wall on the ball is:

1. \(2000\ \text{N}\)
2. \(1000\ \text{N}\)
3. \(5000\ \text{N}\)
4. \(125\ \text{N}\)

A particle moves in the \(XY\text-\)plane under the action of a force \(F\) such that the components of its linear momentum \(p\) at any time \(t\) are \(p_x = 2 \cos t\),  \(p_y = 2 \sin t\). The angle between \(F\) and \(p\) at time \(t\) will be:

Swimming is possible on account of:

1. First law of motion
2. Second law of motion
3. Third law of motion
4. Newton's law of gravitation

On a stationary sailboat, the air is blown at the sails from a fan attached to the boat. The boat will:

1. remain stationary

2. spin around

3. move in a direction opposite to that in which air is blown

4. move in the direction in which the air is blown

A man is standing on a spring platform. The reading of the spring balance is \(60\ \text{kg-wt}\). If a man jumps off the platform, then the reading of the spring balance:

1. first increases, then decreases to zero.

2. decreases.

3. increases.

4. remains the same.

The tension in the spring shown in the figure is:

1. Zero
2. \(2.5\ \text{N}\)
3. \(5\ \text{N}\)
4. \(10\ \text{N}\)