A block of mass \(m\) is placed on a smooth wedge of inclination \(θ\). The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block will be: 

1. \(mg\cos 𝜃\)
2. \(mg\sin 𝜃\)
3. \(mg\)
4. \(\dfrac{mg}{\cos 𝜃}\)

The linear momentum \(p\) of a body moving in one dimension varies with time according to the equation \(p = a + bt^2\) where \(a\) and \(b\) are positive constants. The net force acting on the body is:

1. A constant
2. Proportional to \(t^2\)
3. Inversely proportional to \(t\)
4. Proportional to \(t\)

A man of mass \(80\ \text{kg}\) is standing in an elevator that is moving with an acceleration of \(6\ \text{m/s}^2\) in the upward direction. The apparent weight of the man will be \((\text{Take} \ g = 10\ \text{m/s}^2)\):

1. \(1480\ \text{N}\)
2. \(1280\ \text{N}\)
3. \(1380\ \text{N}\)
4. None of these

\(N\) bullets, each of mass \(m\ \text{kg}\) are fired with a velocity \(v\ \text{ms}^{–1}\) at the rate of \(n\) bullets per second upon a wall. The reaction offered by the wall on the bullets is given by:

1. \(nmv\)

2. \(\dfrac{Nmv}n\)$\frac{}{}$

3. \(n\dfrac{Nm}v\)$$

4. \(n\dfrac{Nv}m\)$$

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: