1
JEE Main 2024 (Online) 1st February Morning Shift
Numerical
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The identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is ___________ .
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2
JEE Main 2024 (Online) 31st January Morning Shift
Numerical
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A solid circular disc of mass $$50 \mathrm{~kg}$$ rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \mathrm{~m} / \mathrm{s}$$. The absolute value of work done on the disc to stop it is ________ J.

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3
JEE Main 2024 (Online) 31st January Morning Shift
Numerical
+4
-1
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A body starts falling freely from height $$H$$ hits an inclined plane in its path at height $$h$$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $$\frac{H}{h}$$ for which the body will take the maximum time to reach the ground is __________.

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4
JEE Main 2023 (Online) 8th April Morning Shift
Numerical
+4
-1
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The momentum of a body is increased by $$50 \%$$. The percentage increase in the kinetic energy of the body is ___________ $$\%$$.

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