Using the method of dimensions, check the correctness of the following equations: v = F m , where v is the velocity of a transverse wave in a string of mass per unit length m and stretched under tension F .

Consider the equation v = F m ,where v is the velocity of a transverse wave in a string of mass per unit length m and stretched under tension F . Dimension of the terms on the L.H.S of the equation i.e.velocity v = [ M 0 L 1 T - 1 ] Dimension of the terms on the R.H.S of the equation i.e. F m = [ M 1 L 1 T - 2 ] ] [ M 1 L - 1 T 0 ] = [ M 0 L 2 T - 2 ] 1 2 = [ M 0 L 1 T - 1 ] Dimension of the terms on the L.H.S=Dimension of the terms on the R.H.S Hence, according to the principle of dimensional homogeneity, the equation is dimensionally correct.

Using the method of dimensions, check the correctness of the following equations: v = F m , where v is the velocity of a transverse wave in a string of mass per unit length m and stretched under tension F .

Consider the equation v = F m ,where v is the velocity of a transverse wave in a string of mass per unit length m and stretched under tension F . Dimension of the terms on the L.H.S of the equation i.e.velocity v = [ M 0 L 1 T - 1 ] Dimension of the terms on the R.H.S of the equation i.e. F m = [ M 1 L 1 T - 2 ] ] [ M 1 L - 1 T 0 ] = [ M 0 L 2 T - 2 ] 1 2 = [ M 0 L 1 T - 1 ] Dimension of the terms on the L.H.S=Dimension of the terms on the R.H.S Hence, according to the principle of dimensional homogeneity, the equation is dimensionally correct.

Using the method of dimensions, check the correctness of the following equations: v = B ρ , where v is the velocity of a longitudinal wave in a liquid of bulk modulus of elasticity B and density ρ .

Consider the equation v = B ρ ,where v is the velocity of a longitudinal wave in a liquid of bulk modulus of elasticity B and density ρ . Dimension of the terms on the L.H.S of the equation i.e.velocity v = [ M 0 L 1 T - 1 ] Dimension of the terms on the R.H.S of the equation i.e. B ρ = [ M 1 L - 1 T - 2 ] ] [ M 1 L - 3 T 0 ] = [ M 0 L 2 T - 2 ] 1 2 = [ M 0 L 1 T - 1 ] Dimension of the terms on the L.H.S=Dimension of the terms on the R.H.S Hence, according to the principle of dimensional homogeneity, the equation is dimensionally correct.

Using the method of dimensions, check the correctness of the following equations: λ = h m v , where λ is the de Broglie wavelength of a particle of m moving with velocity ν .

Consider the equation λ = h mv ,where λ is the de Broglie wavelength of a particle of m moving with velocity ν . Dimension of the terms on the L.H.S of the equation i.e.wavelength λ = [ M 0 L 1 T 0 ] Dimension of the terms on the R.H.S of the equation i.e. h mv = [ M 1 L 2 T - 1 ] [ M 1 L 1 T - 1 ] = [ M 0 L 1 T 0 ] Dimension of the terms on the L.H.S=Dimension of the terms on the R.H.S Hence, according to the principle of dimensional homogeneity, the equation is dimensionally correct.

E M B I B E

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 14

MEDIUM

11th ICSE

IMPORTANT

Earn 100

Using the method of dimensions, check the correctness of the following equations:

$v = \sqrt{\frac{F}{m}}$ , where $v$ is the velocity of a transverse wave in a string of mass per unit length $m$ and stretched under tension $F$ .

Important Questions on Dimensional Analysis

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 14

Using the method of dimensions, check the correctness of the following equations:

$v = \sqrt{\frac{B}{ρ}}$ , where $v$ is the velocity of a longitudinal wave in a liquid of bulk modulus of elasticity $B$ and density $ρ$ .

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 14

Using the method of dimensions, check the correctness of the following equations:

$λ = \frac{h}{m v}$ , where $λ$ is the de Broglie wavelength of a particle of $m$ moving with velocity $ν$ .

HARD

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 15

Prove with the help of dimensional analysis that the equation $h = \frac{1}{2} g t$ for the distance travelled by a body falling freely under gravity in time $t$ is incorrect. Find the correct equation with the help of dimensions.

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 16

Show dimensionally that the equation of the time-period of a simple pendulum of length $l$ , is given by $t = 2 π \sqrt{\frac{l}{g}}$ . .

HARD

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 17

Check the correctness of the relation $h = \frac{r ρ g}{2 S}$ for the height of a liquid of density $ρ$ and surface tension $S$ , raised in a capillary tube of radius $r$ and angle of contact zero with the liquid. If incorrect, then deduce the correct form.

HARD

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 18

A particle of mass $m$ is tied to a string and swung around in a circular path of radius $r$ with a constant speed $v .$ Derive a formula for the centripetal force $F$ exerted by the particle on our hand, using the method of dimensions.

HARD

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 19

The energy $E$ of a particle oscillating in S.H.M depends on the mass $m$ of the particle, frequency $n$ and amplitude $a$ of oscillation. Show dimensionally that $E \propto m n^{2} a^{2} .$

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 5 - Dimensional Analysis>NUMERICALS>Q 20

The velocity of transverse waves along a string may depend upon the length $l$ of the string, tension $f$ in the string and mass per unit length $m$ of the string. Derive a possible formula for the velocity dimensionally.