1
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1

The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $$\rho=\rho_{0}\left(1-\frac{x^{2}}{L^{2}}\right) \mathrm{kg} / \mathrm{m}$$ and length L (in meter) is $$\frac{3 L}{\alpha} \mathrm{m}$$. The value of $$\alpha$$ is ___________. (where x is the distance from end A)

2
JEE Main 2022 (Online) 25th July Evening Shift
Numerical
+4
-1

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $$\sqrt x$$ m. The value of x is ____________.

3
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms$$-$$1. The velocity of the running man was ___________ ms$$-$$1, when he jumps into the car.

4
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms$$-$$1. The impulse imparted to the ball is ___________ Ns.