Advertisements
Advertisements
प्रश्न
Derive the formula of the kinetic energy of a particle having mass ‘m’ and velocity ‘v’, using dimensional analysis.
Advertisements
उत्तर
The kinetic energy of a body depends upon mass (m) and velocity (v) of the body.
Let K.E. ∝ mx vy
∴ K.E. = kmx vy ...(1)
where,
k = dimensionless constant of proportionality.
Taking dimensions on both sides of equation (1),
[L2M1T-2]
= [L0 M1 T0]x [L1 M0 T-1]y
= [L0 Mx T0] [Ly M0 T-y]
= `["L"^(0+y) " M"^(x + 0) " T"^(0- y)]`
[L2 M1 T-2] = [Ly Mx T-y] ...(2)
Equating dimensions of L, M, T on both sides of equation (2),
x = 1 and y = 2
Substituting x, y in equation (1), we have
K.E. = kmv2
APPEARS IN
संबंधित प्रश्न
It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1 s?
Answer the following question.
What are the dimensions of the quantity `lsqrt(l//g)`, l being the length, and g the acceleration due to gravity?
An electron with charge e enters a uniform magnetic field `vec"B"` with a velocity `vec"v"`. The velocity is perpendicular to the magnetic field. The force on the charge is given by `|vec"F"|`= B e v.
Obtain the dimensions of `vec"B"`.
An object is falling freely under gravitational force. Its velocity after travelling a distance h is v. If v depends upon gravitational acceleration g and distance, prove with the dimensional analysis that v = k`sqrt"gh"` where k is a constant.
v = `at + b/(t + c) + "v"_0` is a dimensionally valid equation. Obtain the dimensional formula for a, b and c where v is velocity, t is time and v0 is initial velocity.
Which of the following time measuring devices is most precise?
What was the original scientific basis for defining one second?
What specific characteristic of cesium-133 atoms makes them ideal for modern timekeeping?
How many vibrations of cesium-133 radiation occur in exactly one second?
Which of the following would be most affected by a timing error in atomic clocks?
How many vibrations of cesium-133 radiation occur in exactly one second?
What is the fundamental unit of time in the SI system?
