1
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

A force $$\mathrm{F}=\left(5+3 y^{2}\right)$$ acts on a particle in the $$y$$-direction, where $$\mathrm{F}$$ is in newton and $$y$$ is in meter. The work done by the force during a displacement from $$y=2 \mathrm{~m}$$ to $$y=5 \mathrm{~m}$$ is ___________ J.

2
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

A small particle moves to position $$5 \hat{i}-2 \hat{j}+\hat{k}$$ from its initial position $$2 \hat{i}+3 \hat{j}-4 \hat{k}$$ under the action of force $$5 \hat{i}+2 \hat{j}+7 \hat{k} \mathrm{~N}$$. The value of work done will be __________ J.

3
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

A lift of mass $$\mathrm{M}=500 \mathrm{~kg}$$ is descending with speed of $$2 \mathrm{~ms}^{-1}$$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $$2 \mathrm{~ms}^{-2}$$. The kinetic energy of the lift at the end of fall through to a distance of $$6 \mathrm{~m}$$ will be _____________ $$\mathrm{kJ}$$.

4
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
A body of mass $2 \mathrm{~kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in $4 \mathrm{~s}$ is $\frac{1}{3} \alpha^{2} \sqrt{P} m$. The value of $\alpha$ will be ______.