Particles of masses 1 g, 2 g, 3 g,...... , 100 g are kept at the marks 1 cm, 2 cm, 3 cm,....... , 100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

Particles of masses 1 g, 2 g, 3 g,...... , 100 g are kept at the marks

1.	Particles of masses 1 g, 2 g, 3 g,...... , 100 g are kept at the marks 1 cm, 2 cm, 3 cm,....... , 100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.
Answer» Masses of 1 gm, 2 gm ……100 gm are kept at the marks 1 cm, 2 cm, ……1000 cm on he x axis respectively. A perpendicular axis is passed at the 50th particle. Therefore on the L.H.S. side of the axis there will be 49 particles and on the R.H.S. side there are 50 particles. Consider the two particles at the position 49 cm and 51 cm. Moment inertial due to these two particle will be = 49 × 1² + 51 + 1² = 100 gm-cm² Similarly if we consider 48th and 52nd term we will get 100 ×2²gm-cm² Therefore we will get 49 such set and one lone particle at 100 cm. Therefore total moment of inertia = 100 {1² + 2² + 3² + … + 49²} + 100(50)². = 100 × (50 × 51 × 101)/6 = 4292500 gm-cm² = 0.429 kg-m² = 0.43 kg-m².

Discussion

No Comment Found

Related InterviewSolutions

A wheel of radius 20 cm is pushed to move it on a rough horizontal surface. It is found to move through a distance of 60 cm on they road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is(a) along the velocity of the wheel(b) opposite to the velocity of the wheel(c) perpendicular to the velocity of the wheel(d) zero.
A body is in pure rotation. The linear speed v of a particle, the distance r of the particle from the axis and the angular velocity ω of the body are related asω = v/r. thus(a) ω ∝1/r(b) ω ∝ r(c) ω = 0(d) ω is independent of r.
A sphere is rolled on a rough horizontal surface. It gradually slows down and stops. The force of friction tries to(a) decrease the linear velocity(b) increase the angular velocity(c) increase the linear momentum(d) decrease the angular velocity.
In rear-wheel drive cars, the engine rotates the rear wheels and the front wheels rotate only because the car moves. If such a car accelerates on a horizontal road, the friction (a) on the rear wheels is in the forward direction (b) on the front wheels is in the backward direction (c) on the rear wheels has larger magnitude than the friction on the front wheels (d) on the car is in the backward direction.
Can an object be in pure translation as well as in pure rotation?
A simple pendulum is a point mass suspended by a light thread from a fixed point. The particle is displaced towards one side and then released. It makes small oscillations. Is the motion of such a simple pendulum a pure rotation? If yes where is the axis of rotation?
If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?
A body rotating at 20 rad/s is acted upon by a constant torque providing it a deceleration of 2 rad/s 2 . At what time will the body have kinetic energy same as the initial value if the torque continues to act ?
A disc of radius 10 cm is rotating about its axis at an angular speed of 20 rad/s. Find the linear speed of(a) a point on the rim,(b) the middle point of a radius.
A sphere can roll on a surface inclined at an angle 0 if the friction coefficient is more than 2/7 g tanθ. Suppose the friction coefficient is 1/7 g tanθ. If a sphere is released from rest on the incline,(a) it will stay at rest(b) it will make pure translational motion(c) it will translate and rotate about the centre(d) the angular momentum of the sphere about its centre will remain constant.

Particles of masses 1 g, 2 g, 3 g,...... , 100 g are kept at the marks 1 cm, 2 cm, 3 cm,....... , 100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment