A car covers AB distance with first one-third at velocity v1ms−1, second one-third at v2ms−1 and last one-third at v3ms−1. If v3=3v1,v2=2v1 and v1=11ms−1, then the average velocity of the car is _____ ms−1.
Held on 28 Jun 2022 · Verified 6 Jul 2026.
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A string $A$ of length $0.314$ m and Young's modulus $2 \times 10^{10}$ N/m$^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8$ kg. The net change in length of the combination is _____ mm. (radius of both the strings is $0.2$ mm and acceleration due to gravity $= 10$ m/s$^2$) (Mass of both strings is to be neglected as compared to the mass of load)
A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F=-k v$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity ($v$) versus time ($t$)?
A spring of force constant $15 \mathrm{~N} / \mathrm{m}$ is cut into two pieces. If the ratio of their length is $1: 3$, then the force constant of smaller piece is $\_\_\_\_$ $\mathrm{N} / \mathrm{m}$.
Initially a satellite of 100 kg is in a circular orbit of radius $1.5 \mathrm{R}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $\alpha \times 10^{6} \mathrm{~J}$ of energy. The value of $\alpha$ is $\_\_\_\_$. (Take Radius of Earth $R_{E}=6 \times 10^{6} \mathrm{~m}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)
A liquid drop of diameter $2$ mm breaks into $512$ droplets. The change in surface energy is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _______. (Take surface tension of liquid $= 0.08$ N/m)
Work through every JEE Main Mechanics PYQ, year by year.