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 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
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 \(x = 1\) cm to \(x = 5\) cm is:
1. \(20\) ergs
2. \(60\) ergs
3. \(70\) ergs
4. \(700\) ergs
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 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:
1. | 30 J | 2. | 15 J |
3. | 25 J | 4. | 20 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:
1. | \(475\) J | 2. | \(450\) J |
3. | \(275\) J | 4. | \(250\) J |
A ball is thrown vertically downwards from a height of 20 m with an initial velocity vo. It collides with the ground, loses 50% of its energy in a collision and rebounds to the same height. The initial velocity vo is: (Take g = 10 ms-2)
1. 14 ms-1
2. 20 ms-1
3. 28 ms-1
4. 10 ms-1
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. \(Mg/2k\)
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.
2.
3.
4.