Velocity of a freely falling body changes as {g^p}{h^q} where g is acceleration due to gravity and h

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

medium

The velocity of a freely falling body changes as ${g^p}{h^q}$ where g is acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are

A

$1,\frac{1}{2}$

B

$\frac{1}{2},\frac{1}{2}$

C

$\frac{1}{2},\,1$

D

$1,\,1$

Solution

(b) $v \propto {g^p}{h^q}$ (given)

By substituting the dimension of each quantity and comparing the powers in both sides we get $[L{T^{ – 1}}] = {[L{T^{ – 2}}]^p}{[L]^q}$

$ \Rightarrow $ $p + q = 1,\,\, – 2p = – 1,\,$

$\therefore \,\,p = \frac{1}{2},\,q = \frac{1}{2}$

Standard 11

Physics

Share

Similar Questions

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is

medium

Let us consider an equation

$\frac{1}{2} m v^{2}=m g h$

where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.

easy

If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck 's constant $h$ are taken as fundamental quantities, the permeability of vacuum $\mu _0$ can be expressed in units of

hard

(JEE MAIN-2015)

If $L,\,C$ and $R$ represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency

medium

(IIT-1984)

The amount of heat energy $Q$, used to heat up a substance depends on its mass $m$, its specific heat capacity $(s)$ and the change in temperature $\Delta T$ of the substance. Using dimensional method, find the expression for $s$ is (Given that $\left.[s]=\left[ L ^2 T ^{-2} K ^{-1}\right]\right)$ is

medium