1
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be $${1 \over 2}\sqrt {xgh}$$ m/s. The value of x is ___________.

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

Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '2R' are as follows:

I1 = M.I. of solid sphere about its diameter

I2 = M.I. of solid cylinder about its axis

I3 = M.I. of solid circular disc about its diameter

I4 = M.I. of thin circular ring about its diameter

If 2(I2 + I3) + I4 = x . I1, then the value of x will be __________.

3
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x $$\times$$ 10$$-$$2 kg. The value of x is ___________.

4
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ____________ ms$$-$$1. (Take g = 10 ms$$-$$2)