JEE Main 2025 Apr 4 Shift 1 — Physics

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)^{\text{th}}$ of its volume. The frequency of the fundamental note will change by

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M^P L^Q T^R A^S}$, where value of 'Q' and 'R' are

Which of the following are correct expression for torque acting on a body?

A. $\vec{\tau} = \vec{r} \times \vec{L}$

B. $\vec{\tau} = \frac{d}{dt}\left(\vec{r} \times \vec{p}\right)$

C. $\vec{\tau} = \vec{r} \times \frac{d\vec{p}}{dt}$

D. $\vec{\tau} = I\,\vec{\alpha}$

E. $\vec{\tau} = \vec{r} \times \vec{F}$

($\vec{r}$ = position vector; $\vec{p}$ = linear momentum; $\vec{L}$ = angular momentum; $\vec{\alpha}$ = angular acceleration; $I$ = moment of inertia; $\vec{F}$ = force; $t$ = time)

Choose the correct answer from the options given below:

A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $\mathrm{T_1}$ and $\mathrm{T_2}$ simultaneously. $\mathrm{T_1}$ and $\mathrm{T_2}$ are related by $\mathrm{T_1} = \sqrt{3}\,\mathrm{T_2}$, the angles $\theta_1$ and $\theta_2$ are

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: The kinetic energy needed to project a body of mass m from earth surface to infinity is $\frac{1}{2}\mathrm{mgR}$, where R is the radius of earth.

Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.

In the light of the above statements, choose the correct answer from the options given below

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass '$m$' having position vector as $\vec{r} = a\left(\hat{i}\,\cos\omega t + \hat{j}\,\sin\omega t\right)$. The direction of force is