ROTATIONAL KINEMATICS, TORQUE, MECHANICAL QUILIBRIUM
Rotational Motion

269560 A particle of mass \(1 \mathrm{~kg}\) is projected with an initial velocity \(10 \mathrm{~ms}^{-1}\) at an angle of projection \(45^{\circ}\) with the horizontal. The average torque acting on the projectile between the time at which it is projected and the time at which it strikes the ground about the point of projection in newton meter is

1 25
2 50
3 75
4 100
Rotational Motion

269561 A uniform metre scale of mass \(1 \mathrm{~kg}\) is placed on table such that a part of the scale is beyond the edge. If a body of mass \(0.25 \mathrm{~kg}\) is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt is

1 \(30 \mathrm{~cm}\)
2 \(80 \mathrm{~cm}\)
3 \(70 \mathrm{~cm}\)
4 \(60 \mathrm{~cm}\)
Rotational Motion

269562 A heavy wheel of radius \(20 \mathrm{~cm}\) and weight \(10 \mathrm{~kg}\) is to be dragged over a step of height \(10 \mathrm{~cm}\), by a horizontal force \(F\) applied at the centre of the wheel. The minimum value of \(F\) is

1 \(20 \mathrm{kgwt}\)
2 \(1 \mathrm{kgwt}\)
3 \(10 \sqrt{3} \mathrm{kgwt}\)
4 \(10 \sqrt{2} \mathrm{kgwt}\)
Rotational Motion

269610 A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

1 \(4 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
2 \(8 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
3 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
4 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

269560 A particle of mass \(1 \mathrm{~kg}\) is projected with an initial velocity \(10 \mathrm{~ms}^{-1}\) at an angle of projection \(45^{\circ}\) with the horizontal. The average torque acting on the projectile between the time at which it is projected and the time at which it strikes the ground about the point of projection in newton meter is

1 25
2 50
3 75
4 100
Rotational Motion

269561 A uniform metre scale of mass \(1 \mathrm{~kg}\) is placed on table such that a part of the scale is beyond the edge. If a body of mass \(0.25 \mathrm{~kg}\) is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt is

1 \(30 \mathrm{~cm}\)
2 \(80 \mathrm{~cm}\)
3 \(70 \mathrm{~cm}\)
4 \(60 \mathrm{~cm}\)
Rotational Motion

269562 A heavy wheel of radius \(20 \mathrm{~cm}\) and weight \(10 \mathrm{~kg}\) is to be dragged over a step of height \(10 \mathrm{~cm}\), by a horizontal force \(F\) applied at the centre of the wheel. The minimum value of \(F\) is

1 \(20 \mathrm{kgwt}\)
2 \(1 \mathrm{kgwt}\)
3 \(10 \sqrt{3} \mathrm{kgwt}\)
4 \(10 \sqrt{2} \mathrm{kgwt}\)
Rotational Motion

269610 A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

1 \(4 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
2 \(8 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
3 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
4 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

269560 A particle of mass \(1 \mathrm{~kg}\) is projected with an initial velocity \(10 \mathrm{~ms}^{-1}\) at an angle of projection \(45^{\circ}\) with the horizontal. The average torque acting on the projectile between the time at which it is projected and the time at which it strikes the ground about the point of projection in newton meter is

1 25
2 50
3 75
4 100
Rotational Motion

269561 A uniform metre scale of mass \(1 \mathrm{~kg}\) is placed on table such that a part of the scale is beyond the edge. If a body of mass \(0.25 \mathrm{~kg}\) is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt is

1 \(30 \mathrm{~cm}\)
2 \(80 \mathrm{~cm}\)
3 \(70 \mathrm{~cm}\)
4 \(60 \mathrm{~cm}\)
Rotational Motion

269562 A heavy wheel of radius \(20 \mathrm{~cm}\) and weight \(10 \mathrm{~kg}\) is to be dragged over a step of height \(10 \mathrm{~cm}\), by a horizontal force \(F\) applied at the centre of the wheel. The minimum value of \(F\) is

1 \(20 \mathrm{kgwt}\)
2 \(1 \mathrm{kgwt}\)
3 \(10 \sqrt{3} \mathrm{kgwt}\)
4 \(10 \sqrt{2} \mathrm{kgwt}\)
Rotational Motion

269610 A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

1 \(4 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
2 \(8 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
3 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
4 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

269560 A particle of mass \(1 \mathrm{~kg}\) is projected with an initial velocity \(10 \mathrm{~ms}^{-1}\) at an angle of projection \(45^{\circ}\) with the horizontal. The average torque acting on the projectile between the time at which it is projected and the time at which it strikes the ground about the point of projection in newton meter is

1 25
2 50
3 75
4 100
Rotational Motion

269561 A uniform metre scale of mass \(1 \mathrm{~kg}\) is placed on table such that a part of the scale is beyond the edge. If a body of mass \(0.25 \mathrm{~kg}\) is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt is

1 \(30 \mathrm{~cm}\)
2 \(80 \mathrm{~cm}\)
3 \(70 \mathrm{~cm}\)
4 \(60 \mathrm{~cm}\)
Rotational Motion

269562 A heavy wheel of radius \(20 \mathrm{~cm}\) and weight \(10 \mathrm{~kg}\) is to be dragged over a step of height \(10 \mathrm{~cm}\), by a horizontal force \(F\) applied at the centre of the wheel. The minimum value of \(F\) is

1 \(20 \mathrm{kgwt}\)
2 \(1 \mathrm{kgwt}\)
3 \(10 \sqrt{3} \mathrm{kgwt}\)
4 \(10 \sqrt{2} \mathrm{kgwt}\)
Rotational Motion

269610 A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

1 \(4 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)
2 \(8 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
3 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 40 \pi \mathrm{rad} / \mathrm{s}\)
4 \(6 \pi \mathrm{rad} / \mathrm{s}^{2}, 80 \pi \mathrm{rad} / \mathrm{s}\)