1
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $$\sqrt x$$ cm. The value of $$x$$ is ________.

2
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1

Four identical discs each of mass '$$\mathrm{M}$$' and diameter '$$\mathrm{a}$$' are arranged in a small plane as shown in figure. If the moment of inertia of the system about $$\mathrm{OO}^{\prime}$$ is $$\frac{x}{4} \,\mathrm{Ma}^{2}$$. Then, the value of $$x$$ will be ____________.

3
JEE Main 2022 (Online) 27th July Evening Shift
Numerical
+4
-1

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $$4 \mathrm{~ms}^{-1}$$, is ____________ cm. (take g = $$10 \mathrm{~ms}^{-2}$$)

4
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1

A pulley of radius $$1.5 \mathrm{~m}$$ is rotated about its axis by a force $$F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\right) N$$ applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is $$4.5 \mathrm{~kg} \mathrm{~m}^{2}$$, the number of rotations made by the pulley before its direction of motion is reversed, will be $$\frac{K}{\pi}$$. The value of K is ___________.

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