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JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1 A uniform disc of mass $0.5 \mathrm{~kg}$ and radius $r$ is projected with velocity $18 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=0$ s on a rough horizontal surface. It starts off with a purely sliding motion at $\mathrm{t}=0 \mathrm{~s}$. After $2 \mathrm{~s}$ it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after $2 \mathrm{~s}$ will be __________ $\mathrm{J}$ (given, coefficient of friction is $0.3$ and $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ). 2
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1 The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2}=50-x^{2}$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is ___________. $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
3
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1 A body of mass $2 \mathrm{~kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in $4 \mathrm{~s}$ is $\frac{1}{3} \alpha^{2} \sqrt{P} m$. The value of $\alpha$ will be ______.
4
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1 A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \mathrm{~s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11} \mathrm{~s}$. The value of $\alpha$ is __________.