The potential energy of a particle varies wit | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(a)

$x =$ distance from a fixed origin

$u =\frac{ A \sqrt{ x }}{ x ^2+ B }$

unit of $B$ is same as $x ^2$. Unit of $x ^2=\left[ L ^2\right]$

Vedclass · Accepted Answer

$\left[ ML ^{11/2} T ^{-2}\right]$

Vedclass · Answer

(a)

$x =$ distance from a fixed origin

$u =\frac{ A \sqrt{ x }}{ x ^2+ B }$

unit of $B$ is same as $x ^2$. Unit of $x ^2=\left[ L ^2ight]$

$B =\left[ L ^2ight]$

$u =\frac{\left[ x ^{1 / 2}ight] A }{ x ^2+ B }$

$A =\frac{ u \left( x ^2+ B ight)}{\sqrt{ x }}=\frac{ kgm }{ s ^2} 	imes \frac{ m ^2}{ m ^{1 / 2}}$

$A =\frac{ kgm }{ s ^2}$

$A =\left[ ML ^{7 / 2} T ^{-2}ight]$

Dimensions of $AB =\left[ ML ^{7 / 2} T ^{-2}ight]\left[ L ^2ight]$

Dimensions of $AB =\left[ ML ^{11 / 2} T ^{-2}ight]$

	List $-I$		List $-II$
$A$.	Coefficient of Viscosity	$I$.	$[M L^2T^{–2}]$
$B$.	Surface Tension	$II$.	$[M L^2T^{–1}]$
$C$.	Angular momentum	$III$.	$[M L^{-1}T^{–1}]$
$D$.	Rotational Kinetic energy	$IV$.	$[M L^0T^{–2}]$

List I	List II
$(i)$ Curie	$(A)$ $ML{T^{ - 2}}$
$(ii)$ Light year	$(B)$ $M$
$(iii)$ Dielectric strength	$(C)$ Dimensionless
$(iv)$ Atomic weight	$(D)$ $T$
$(v)$ Decibel	$(E)$ $M{L^2}{T^{ - 2}}$
	$(F)$ $M{T^{ - 3}}$
	$(G)$ ${T^{ - 1}}$
	$(H)$ $L$
	$(I)$ $ML{T^{ - 3}}{I^{ - 1}}$
	$(J)$ $L{T^{ - 1}}$

The potential energy of a particle varies with distance $x$ from a fixed origin as $U=\frac{A \sqrt{x}}{x^2+B}$, where $A$ and $B$ are dimensional constants then dimensional formula for $A B$ is

Similar Questions

The equation of stationary wave is

$\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)$

Which of the following is NOT correct

Match List $-I$ with List $-II$

List $-I$ List $-II$

$A$. Coefficient of Viscosity $I$. $[M L^2T^{–2}]$

$B$. Surface Tension $II$. $[M L^2T^{–1}]$

$C$. Angular momentum $III$. $[M L^{-1}T^{–1}]$

$D$. Rotational Kinetic energy $IV$. $[M L^0T^{–2}]$

Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is