Home
Class 11
PHYSICS
The self inductance L of a solenoid of l...

The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as

Text Solution

Verified by Experts

The forces acting om the plank are shown in the figure. The height of water gravity of the plank is 0.5. Find the angle 0 the pank 1.0=2l. The weight of the plank acts throught he centre B of the plank. We have `OB=` The buoyant force F acts through the point A which is the middle point of the dipped part OC of the plank.
We have `OA=(OC)/(2)=(l)/(2costheta)`
Let the mass per unit length of the plank be `rho`. its weight `mg=2lrhog`.
The mass of the part OC of the plank `=((l)/(costheta))rho`.
the mass of water displaced `=(1)/(0.5)(l)/(costheta)rho(2lrho)/(costheta)`
The buoyant force F is therefore `F=(2lrhog)/(costheta)`
Now, for equilibrium the torque of mg about O should balance the torque of F about O.
So, mg `(OB)sintheta=F(OA)sintheta` or , `(2lrho)l=((2lrho)/(costheta))((l)/(2costheta))` or, `cos^(2)theta=(1)/(2)` or `costheta=(1)/(sqrt(2))`, or `theta=45^(@)`
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN |Exercise Exercise 1 (Elasticity)|16 Videos

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN |Exercise Exercise 1 (Surface Tension)|21 Videos

  • CENTRE OF MASS

    ALLEN |Exercise EXERCISE-V B|19 Videos

  • ERROR AND MEASUREMENT

    ALLEN |Exercise Part-2(Exercise-2)(B)|22 Videos

Similar Questions

Explore conceptually related problems

The self inductance angle of a solenoid of length and are of cross section A with a fixed number of turns N increases as,

What is the self inductance of a solenoid of length 31.4 cm., area of cross section 10^(-3) m^2 and total number of turns 10^3 ?

The self-inductance of two solenoids A and B having equal length are same. If the number of turns in two solenoids A and B are 100 and 200 respectively the ratio of the radii of their cross section will be ........

An air-cored solenoid with length 30 cm, area of cross-section 25 "cm"^2 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10^(-3) s. How much is the average back emf induced across the ends of the open switch in the circuit ? Ignore the variation in magnetic field near the ends of the solenoid.

Current I is following through a toroidal solenoid of radius r, length l and area A. If the number of turns of toroidal solenoid is N, then energy stored in the toroidal solenoid is …..

A wire of given material having length l and area of cross-section A has a resistance of 4 n. What would be the resistance of another wire of the same material having length 1/2 and area of cross - section 2A ?

Constant temperature of ends are T_(1) and T_(2) (where T_(1)gtT_(2) ) for a conducting rod of 'L' length and cross-sectional area A. What would be the rate of heat transfer in thermal steady state ?

Consider the two idealized systems : (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L lt lt R , radius of cross-section. In (i) overset(to) is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below :

A steel wire of length 60 cm and area of cross section 10^(-6)m^(2) is joined with a n aluminium wire of length 45 cm and are of cross section 3xx10^(-6)m^(2) . The composite string is stretched by a tension of 80 N. Density of steel is 7800kgm^(-3) and that of aluminium is 2600kgm^(-3) the minimum frequency of tuning fork. Which can produce standing wave in it with node at joint is

A closely wound solenoid of 800 turns and area of cross section 2.5 times 10^-4 m^2 carries a current of 3.0A. Explain the sense in which the solenoid acts like a bar magnet.