(D) According to the theory of relativity,the mass of a particle increases with its speed $v$ as $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$.However,

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If the Assertion is incorrect but the Reason is correct.

(D) According to the theory of relativity,the mass of a particle increases with its speed $v$ as $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$.However,the electric charge of a particle is an invariant quantity and does not change with its speed.Therefore,the Assertion is incorrect because the charge remains constant,while the Reason is correct as it accurately describes the relativistic mass variation.

Class 12 Physics Dual Nature of Radiation and matter Mix Examples-Dual Nature of Radiation and matter

Easy

Assertion: If the speed of a charged particle increases,both the mass and the charge increase.
Reason: If $m_0$ is the rest mass and $m$ is the mass at velocity $v$,then $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$,where $c$ is the speed of light.

AIIMS 2000 All AIIMS

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If the Assertion is incorrect but the Reason is correct.

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Dual Nature of Radiation and matter

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Mix Examples-Dual Nature of Radiation and matter

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AIIMS 2000 Paper All AIIMS years →

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Planck's constant $(h)$ $I$. $[M^1 L^2 T^{-2}]$

$B$. Stopping potential $(V_s)$ $II$. $[M^1 L^1 T^{-1}]$

$C$. Work function $(\phi)$ $III$. $[M^1 L^2 T^{-1}]$

$D$. Momentum $(p)$ $IV$. $[M^1 L^2 T^{-3} A^{-1}]$

List $I$	List $II$
$A$. Planck's constant $(h)$	$I$. $[M^1 L^2 T^{-2}]$
$B$. Stopping potential $(V_s)$	$II$. $[M^1 L^1 T^{-1}]$
$C$. Work function $(\phi)$	$III$. $[M^1 L^2 T^{-1}]$
$D$. Momentum $(p)$	$IV$. $[M^1 L^2 T^{-3} A^{-1}]$

MediumJEE MAIN 2023

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An electron moving with speed $v$ and a photon moving with speed $c$ have the same de Broglie wavelength. The ratio of the kinetic energy of the electron to that of the photon is -

MediumJEE MAIN 2021

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The anode voltage of a photocell is kept constant. The wavelength of the incident light on the cathode is changed gradually. Then,the photoelectric current $I$ of the photocell varies according to which of the following graphs?

Medium

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Light of wavelength $2475 \, Å$ is incident on barium. Photoelectrons emitted describe a circle of radius $100 \, cm$ in a magnetic field of flux density $\frac{1}{\sqrt{17}} \times 10^{-5} \, T$. The work function of the barium is .............. $eV$ (Given $\frac{e}{m} = 1.7 \times 10^{11} \, C/kg$)

Difficult

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When a light source of power $P$ emitting monochromatic light of wavelength $\lambda$ is kept at a distance $r$ from a photosensitive surface of work function $\phi$ and surface area $A$,which of the following is the wrong option?

Medium

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Assertion: If the speed of a charged particle increases,both the mass and the charge increase.Reason: If $m_0$ is the rest mass and $m$ is the mass at velocity $v$,then $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$,where $c$ is the speed of light.

Similar Questions

Match List $I$ with List $II$: List $I$ List $II$ $A$. Planck's constant $(h)$ $I$. $[M^1 L^2 T^{-2}]$ $B$. Stopping potential $(V_s)$ $II$. $[M^1 L^1 T^{-1}]$ $C$. Work function $(\phi)$ $III$. $[M^1 L^2 T^{-1}]$ $D$. Momentum $(p)$ $IV$. $[M^1 L^2 T^{-3} A^{-1}]$

An electron moving with speed $v$ and a photon moving with speed $c$ have the same de Broglie wavelength. The ratio of the kinetic energy of the electron to that of the photon is -

The anode voltage of a photocell is kept constant. The wavelength of the incident light on the cathode is changed gradually. Then,the photoelectric current $I$ of the photocell varies according to which of the following graphs?

When a light source of power $P$ emitting monochromatic light of wavelength $\lambda$ is kept at a distance $r$ from a photosensitive surface of work function $\phi$ and surface area $A$,which of the following is the wrong option?

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Assertion: If the speed of a charged particle increases,both the mass and the charge increase.
Reason: If $m_0$ is the rest mass and $m$ is the mass at velocity $v$,then $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$,where $c$ is the speed of light.

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Planck's constant $(h)$ $I$. $[M^1 L^2 T^{-2}]$

$B$. Stopping potential $(V_s)$ $II$. $[M^1 L^1 T^{-1}]$

$C$. Work function $(\phi)$ $III$. $[M^1 L^2 T^{-1}]$

$D$. Momentum $(p)$ $IV$. $[M^1 L^2 T^{-3} A^{-1}]$