1
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 ____________.

2
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.

3
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.

4
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = ____________ m/s so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m/s2)