A man pushes a wall and fails to displace it. He does:
1. negative work
2. positive but not maximum work
3. no work at all
4. maximum work
The minimum work done in pulling up a block of wood weighing \(2\) kN for a length of \(10\) m on a smooth plane inclined at an angle of \(15^\circ\) with the horizontal is (given: \(\mathrm{sin}15^\circ=0.2588)\):
1. \(4.36\) kJ
2. \(5.17\) kJ
3. \(8.91\) kJ
4. \(9.82\) kJ
A spherical ball of mass \(20\) kg is stationary at the top of a hill of height\(100\) m. It slides down a smooth surface to the ground, then climbs up another hill of height \(30\) m and finally slides down to a horizontal base at a height of \(20\) m above the ground. The velocity attained by the ball is:
1. \(10 \) m/s
2. \(10 \sqrt{30} \) m/s
3. \(40 \) m/s
4. \(20 \) m/s
A quarter horse-power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be:
1. 7.46 J
2. 7400 J
3. 7.46 ergs
4. 74.6 J
A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on the table is:
1. \(MgL\)
2. \(MgL/3\)
3. \(MgL/9\)
4. \(MgL/18\)
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.
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