Home
Class 12
PHYSICS
A rod moves lengthwise with a constant v...

A rod moves lengthwise with a constant velocity v relative to the inertial reference frame `K`. At what value of v will the length of the rod in this frame be `eta=0.5%` less than its proper length?

Text Solution

Verified by Experts

From the formula for length contraction
`(l_0-l_0sqrt(1-v^2/c^2))=etal_0`
So, `1-v^2/c^2=(1-eta)^2` or `v=csqrt(eta(2-eta))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PHYSICAL FUNDAMENTALS OF MECHANICS

    IE IRODOV, LA SENA & SS KROTOV|Exercise Hydrodynamics|25 Videos
  • OSCILLATIONS AND WAVES

    IE IRODOV, LA SENA & SS KROTOV|Exercise Electromagnetic Waves, Radiation|36 Videos
  • THERMODYNAMICS AND MOLECULAR PHYSICS

    IE IRODOV, LA SENA & SS KROTOV|Exercise Transport Phenomena|38 Videos

Similar Questions

Explore conceptually related problems

The reference frame, in which the centre of inertia of a given system of particles is at rest, translates with a velocity V relative to an inertial reference frame K. The mass of the system of particles equals m, and the total energy of the system in the frame of the centre of inertia is equal to overset~E . Find the total energy E of this system of particles in the reference frame K.

Two rods having the same proper length l_0 move lengthwise toward each other parallel to a common axis with the same velocity v relative to the laboratory frame of reference. What is the length of each rod in the reference frame fixed to the other rod?

Knowledge Check

  • A vertical rod of length l is moved with constant velocity v towards east. The vertical component of earth magnetic field is B and angle of dip is theta . The induced e.m.f. in the rod is

    A
    `Blv sin theta`
    B
    `Blv tan theta`
    C
    `Blv cot theta`
    D
    `Blv cos theta`
  • Similar Questions

    Explore conceptually related problems

    The frame K^' moves with a constant velocity V relative to the frame K. Find the acceleration w^' of a particle in the frame K^' , if in the frame K this particle moves with a velocity v and acceleration w along a straight line (a) in the direction of the vector V, (b) perpendicular to the vector V.

    In an inertial reference frame K there is only a unifrom electric field E = 8 kV//m in strength. Find the modulus and direction (a) of the vector E' (b) of the vector B' in the interial refrernce frame K' moving with a constant velocity v relative to the frame K at an angle alpha = 45^(@) to the vector E . The velocity of the frame K' is equla to a beta = 0.60 fraction of the velocity of light.

    The density of a stationary body is equal to rho_0 . Find the velocity (relative to the body) of the reference frame in which the density of the body is eta=25% greater than rho_0 .

    A rod flies with constant velocity past a mark which is stationary in the reference frame K. In the frame K it takes Deltat=20ns for the rod to fly past the mark. In the reference frame fixed to the rod the mark moves past the rod of Deltat^'=25ns . Find the proper length of rod.

    A rod moves along a ruler with a constant velocity. When the positions of both ends of the rod are marked simultaneously in the reference frame fixed to the rule, the difference of readings on the rule is equal to Deltax_1=4.0m . But when the positions of the rod's ends are marked simultaneously in the reference frame fixed to the rod, the difference of readings on the same ruler is equal to Deltax_2=9.0m . Find the proper length of the rod and its velocity relative to the ruler.

    The rod A^'B^' moves with a constant velocity v relative to the rod AB (figure). Both rods have the same proper length l_0 and at the ends of each of them clocks are mounted, which are synchronized pariwise: A with B and A^' with B^' . Suppose the moment when the clock B^' gets opposite the clock A is taken for the beginning of the time count in the reference frames fixed to each of the rods. Determine: (a) the readings of the clocks B and B^' at the moment when they are opposite each other, (b) the same for the clocks A and A^' .

    With what velocity (relative to the reference frame K) did the clock move, if during the time interval t=5.0s , measured by the clock of the frame K, it becomes slow by Deltat=0.10s ?