Home
Class 12
PHYSICS
Find the velocity of the moving rod at t...

Find the velocity of the moving rod at time `t` if the initial velocity of the rod is zero and `a` constant force `F` is applied on the rod.Neglect the resistance of the rod.

Text Solution

Verified by Experts

At any time , let the velocity of the rod be v .
Applying Newtons law: F-iIB=ma…..(1)
Also `Biv=i_(1)R=(q)/( c)`
Applying Kcl, `i=i_(1)+(dq)/(dt)=(BlV)/( R)+(D)/(Dt)(BIvC) or i=(B l V)/( R)+B l C a `
Putting the value of `i` in eq. (1), `F-(B^(2)l^(2)V)/( R)=(m+B^(2)l^(2)C)a=(m+B^(2)l^(2)C)(dv)/(dt)`
`(m+B^(2)l^(2)C)(v)/(F-(B^(2)I^(2)v)/( R))=dt`
Integrating both sides, and solving we get `v=(FR)/(B^(2)l^(2))(1-e^((tB^(2)l^(2))/(R(m+CB^(2)l^(2)))))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Two long parallel horizontal rails a, a distance d aprt and each having a risistance lambda per unit length are joing at one end by a resistance R. A perfectly conduction rod MN of mass m is free to slide along the rails without friction (see figure). There is a uniform magnetic field of induction B normal to the plane of the paper and directed into the paper. A variable force F is applied to the rod MN such that, as the rod moves a constant current flows through R. (i) Find the velocity of the rod and the applied force F as function of the distance x of the rod from R. (ii) What fraction of the work done per second by F is converted into heat?

A uniform rod of mass m and length l is pivoted smoothly at O . A horizontal force acts at the bottom of the rod. a. Find the angular velocity of the rod as the function of angle of rotation theta. b.What is the maximum angular displacement of the rod?

For what value of x , the point P on the rod of length l = 6 m has zero acceleration if a force F is applied at the end of rod as shown.

A rod is rotating with angular velocity omega about axis AB. Find costheta .

Figure shows a rigid rod of length 1.0 m. It is pivoted at O. For what value m, the rod will be in equilibrium ? Find the force (F) exerted on the rod by the pivot. Neglect the weight of the rod.

A uniform rod of length l and mass 2m rests on a smooth horizontal table. A point mass m moving horizontally at right angles to the rod with initial velocity v collides with one end of the rod and sticks to it. Determine the position of the point on the rod which remains stationary immediately after collision.

A smooth uniform rod of length L and mass M has two identical beads of negligible size each of mass m which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with an angular velocity omega_0 about an axis perpendicular to the rod and passing through the midpoint of the rod. There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is ......

A conducting circular loop of radius a and resistance per unit length R is moving with a constant velocity v_0 , parallel to an infinite conducting wire carrying current i_0 . A conducting rod of length 2a is approaching the centre of the loop with a constant velocity v_0/2 along the direction 2 of the current. At the instant t = 0 , the rod comes in contact with the loop at A and starts sliding on the loop with the constant velocity. Neglecting the resistance of the rod and the self-inductance of the circuit, find the following when the rod slides on the loop. (a) The current through the rod when it is at a distance of (a/2) from the point A of the loop. (b) Force required to maintain the velocity of the rod at that instant.

A rod AB is moving on a fixed circle of radius R with constant velocity 'v' as shown in figure. P is the point of intersection of the rod and the circle. At an instant the rod is at a distance x=(3R)/(5) from centre of the circle. The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD . (a) Find the speed of point of intersection P (b) Find the angular speed of point of intersection P with respect to centre of the circle.

A rod AB is moving on a fixed circle of radius R with constant velocity v as shown in figure. P is the point of intersection of the rod and the circle. At an instant the rod is at a distance x=(3R)/(5) from centre of the circle. The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD. (i) Find the speed of point of intersection P. (b) Find the angular speed of point of intersection P with respect to centre of the circle.