A particle moves from a point \((-2\hat i+5\hat j)~\text{to}~(4\hat j +3\hat k)\) when a force of \((4\hat i +3\hat j)~\text{N}\) is applied. How much work has been done by the force?
1. \(8~\text{J}\)
2. \(11~\text{J}\)
3. \(5~\text{J}\)
4. \(2~\text{J}\)

A block of mass \(10\) kg, moving in the \(x\text-\)direction with a constant speed of \(10\) ms^-1, is subjected to a retarding force \(F=0.1x\) J/m during its travel from \(x =20\) m to \(30\) m. Its final kinetic energy will be:

A ball is thrown vertically downwards from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision and rebounds to the same height. The initial velocity \(v_0\) is: (Take \(g = 10~\text{m/s}^2\))
1. \(14~\text{m/s}\)
2. \(20~\text{m/s}\)
3. \(28~\text{m/s}\)
4. \(10~\text{m/s}\)

A block of mass \(M\) is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of \(k.\) The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:
1. \(Mg/k\)
2. \(2Mg/k\)
3. \(4Mg/k\)
4. \(Mg/2k\)

The relationship between the force F and the position x of a body is as shown in the figure. The work done in displacing the body from x = 1 m to x = 5 m will be:

The graph between the resistive force \(F\) acting on a body and the distance covered by the body is shown in the figure. The mass of the body is \(25\) kg and the initial velocity is \(2\) m/s. When the distance covered by the body is \(4\) m, its kinetic energy would be:

   
1.   \(50\) J
2. \(40\) J
3. \(20\) J
4.   \(10\) J

The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from \(x = 1~\text{cm}\) to \(x = 5~\text{cm}\) is:
      
1.   \(20~\text{ergs}\) 
2.   \(60~\text{ergs}\)
3.   \(70~\text{ergs}\) 
4.   \(700~\text{ergs}\)

A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then:

1. Lorry will come to rest in a shorter distance

2. Car will come to rest in a shorter distance

3. Both will come to rest in a same distance

4. None of the above

A force \(F = -k(y\hat i +x\hat j)\) (where \(k\) is a positive constant) acts on a particle moving in the \(xy\text-\)plane. Starting from the origin, the particle is taken along the positive \(x\text-\)axis to the point \((a,0)\) and then parallel to the \(y\text-\)axis to the point \((a,a)\). The total work done by the force on the particle is:
1. \(-2ka^2\)
2. \(2ka^2\)
3. \(-ka^2\)
4. \(ka^2\)

A particle of mass 'm' is moving in a horizontal circle of radius 'r' under a centripetal force equal to –K/r², where K is a constant. The total energy of the particle will be:

1. $\frac{K}{2r}$

2. $-\frac{K}{2r}$

3. $-\frac{K}{r}$

4. $\frac{K}{r}$