A force of 5 N making an angle $\theta$ with the horizontal acting on an object displaces it by 0.4 m along the horizontal direction. If the object gains kinetic energy of 1 J then the component of the force is:

The bob of a simple pendulum having length \(l,\) is displaced from the mean position to an angular position \(\theta\) with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. \(\sqrt{2 g l \left(\right. 1 - \cos \theta \left.\right)}\)
2. \(\sqrt{2 g l \left(\right. 1 + \cos\theta)}\)
3. \(\sqrt{2 g l\cos\theta}\)
4. \(\sqrt{2 g l}\)

A block is carried slowly up an inclined plane. If \(W_f\) is work done by the friction, \(W_N\)${\mathrm{}}_{}$ is work done by the reaction force, \(W_g\) is work done by the gravitational force, and \(W_{ex}\) is the work done by an external force, then choose the correct relation(s):
1. \(W _N +   W _f   +   W _g   +   W _{ex}   =   0\)
2. \(W _N   =   0\)
3. \(   W _f   +   W _{ex}   =    - W _g\)
4. All of these

A body of mass 'm' is released from the top of a fixed rough inclined plane as shown in the figure. If the frictional force has magnitude F, then the body will reach the bottom with a velocity: $(\mathrm{L}=\sqrt{2}\mathrm{h})$

A block is released from rest from a height of \(h = 5 ~\text m.\) After traveling through the smooth curved surface, it moves on the rough horizontal surface through a length \(l = 8 ~\text m\) and climbs onto the other smooth curved surface at a height \(h'.\) If $\mathrm{}$\(μ = 0.5,\) then the height \( h'\) is:

A block of mass \(m\) is connected to a spring of force constant \(K.\) Initially, the block is at rest and the spring is relaxed. A constant force \(F\) is applied horizontally towards the right. The maximum speed of the block will be:

                         
1. \(\dfrac{F}{\sqrt{2mK}}\)

2. \(\dfrac{\sqrt{2}F}{\sqrt{mK}}\)

3. \(\dfrac{F}{\sqrt{mK}}\)

4. \(\dfrac{2F}{\sqrt{2mK}}\)