Physics

$\int \dfrac { x d x } { \sqrt { 2 a x - x ^ { 2 } } } = a ^ { n } \sin ^ { - 1 } \left[ \dfrac { x } { a } - 1 \right]$. The value of n is:you may use dimensional analysis to solve the problem

1

SOLUTION
We know,

$\sin^{-1}$ is dimensionless quantity.

And,

$\bigg[\dfrac{x}{a}\bigg]=$ dimensionless.

[x]=[a],

In LHS,

Dimension is $=[a]$

And in RHS,

Dimension is $=[a]^n$

Hence it is clear that $n=1$

Option $\textbf C$ is the correct answer

You're just one step away

Single Correct Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 218

Realted Questions

Q1 Single Correct Medium
The density of a cube is measured by measuring its mass ad length of its side. If the maximum errors in the measurement of its mass and length are $3\%$ and $2\%$ respectively, the maximum error in the measurement of density would be:
• A. $12\%$
• B. $14\%$
• C. $7\%$
• D. $9\%$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Single Correct Medium
Rate of energy dissipation is measured in
• A. Watt
• B. Joule
• C. Weber
• D. Joule / coulomb

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Subjective Medium
In an experiment, the refractive index of glass was observed to be $1.45, 1.56, 1.54, 1.44, 1.54$ and $1.53$. Calculate relative error.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Single Correct Medium
Which of the following do not have the same dimensions as the other three?
Given that: $l=$ length, $m=$ mass, $k=$ force constant, $I=$momet of inertia, $B=$ magnetic induction, ${ P }_{ m } =$ magnetic dipole moment, $R=$ radius and $g=$ acceleration due to gravity
• A. $\sqrt { \dfrac{l}{g }}$
• B. $\sqrt {\dfrac{ I}{{ P }_{ m }B} }$
• C. $\sqrt { \dfrac{k}{m} }$
• D. $\sqrt { \dfrac{R}{g }}$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Medium
The velocity $v$ of a particle at time$t$ is given by $\displaystyle v = at + \frac {b} {t + c}$ where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are respectively :
• A. $LT^{-2}\, , L$ and $\displaystyle T$
• B. $L^{2}\, , T$ and $\displaystyle LT^{2}$
• C. $LT^{2}\, , LT$ and $\displaystyle L$
• D. $L\, , LT$ and $\displaystyle T^{2}$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020