JEE Main 2025 (Online) 29th January Evening Shift

MCQ (Single Correct Answer)

-1

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{dm}{dt} \propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

P $\propto \sqrt{v}$

P $\propto v$

$P^2 \propto v^3$

$P^2 \propto v^5$

JEE Main 2025 (Online) 28th January Evening Shift

MCQ (Single Correct Answer)

-1

A body of mass 4 kg is placed on a plane at a point $P$ having coordinate $(3,4) \mathrm{m}$. Under the action of force $\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}$, it moves to a new point Q having coordinates $(6,10) \mathrm{m}$ in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :

4 : 3

13 : 6

1 : 2

6 : 13

JEE Main 2025 (Online) 28th January Morning Shift

MCQ (Single Correct Answer)

-1

A bead of mass ' $m$ ' slides without friction on the wall of a vertical circular hoop of radius ' $R$ ' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ' $R$ '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' $R$ ', would be (spring constant is ' $k$ ', $g$ is accleration due to gravity)

JEE Main 2025 (Online) 28th January Morning Shift Physics - Work Power & Energy Question 1 English

$\sqrt{2 R g+\frac{\mathrm{kR}^2}{\mathrm{~m}}}$

$\sqrt{3 \mathrm{Rg}+\frac{\mathrm{kR}^2}{\mathrm{~m}}}$

$\sqrt{2 \mathrm{Rg}+\frac{4 \mathrm{kR}^2}{\mathrm{~m}}}$

$2\sqrt{\mathrm{gR}+\frac{\mathrm{kR}^2}{\mathrm{~m}}}$

JEE Main 2025 (Online) 28th January Morning Shift

MCQ (Single Correct Answer)

-1

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A: In a central force field, the work done is independent of the path chosen.

Reason R: Every force encountered in mechanics does not have an associated potential energy.

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

$\mathbf{A}$ is false but $\mathbf{R}$ is true

Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$

$\mathbf{A}$ is true but $\mathbf{R}$ is false

Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$

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