1
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
A ball is dropped from a height of $20 \mathrm{~m}$. If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ________ $\mathrm{m}$.
2
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

A solid sphere of mass $$1 \mathrm{~kg}$$ rolls without slipping on a plane surface. Its kinetic energy is $$7 \times 10^{-3} \mathrm{~J}$$. The speed of the centre of mass of the sphere is __________ $$\operatorname{cm~s}^{-1}$$

3
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1

A particle of mass 100 g is projected at time t = 0 with a speed 20 ms$$^{-1}$$ at an angle 45$$^\circ$$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2s is found to be $$\mathrm{\sqrt K~kg~m^2/s}$$. The value of K is ___________.

(Take g = 10 ms$$^{-2}$$)

4
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ___________ ms$$^{-1}$$.

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