Advertisements
Advertisements
Question
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?
Solution
∴ [g] = `"m"/"s"^2 = ["L"]/["T"^2]`
[k] = `[l sqrt("l"/"g")]`
[k] = [L] `[sqrt("L"/"g")]`
= [L] `[sqrt("L"/[["L"/"T"^2]])]`
= [L] `[sqrt(("LT"^2)/"L")]`
= [L] `[sqrt("T"^2)]`
= [L] [T]
= [L1 T1]
APPEARS IN
RELATED QUESTIONS
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?
Derive the formula of the kinetic energy of a particle having mass ‘m’ and velocity ‘v’, using dimensional analysis.
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.
1.4 times the mass of the sun is equal to
Which of the following time measuring devices is most precise?
