A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid

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4-1.Newton's Laws of Motion

hard

A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L\, (L >> r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure) . If one of the beads is now given a speed $v$, the average force experienced by each support after a long time is (assume all collisions are elastic)

A$\frac{{m{v^2}}}{{2\left( {L - nr} \right)}}$

B$\frac{{m{v^2}}}{{L - 2nr}}$

C$\frac{{m{v^2}}}{{L - nr}}$

Dzero

(JEE MAIN-2015)

Solution

Space between the supports rm for motion of beads is $L – 2nr$
Average force experinced by each support $F = \frac{{2mv}}{{\frac{{2\left( {L – 2nr} \right)}}{V}}} =\frac{{m{V^2}}}{{L – 2nr}}$

Standard 11

Physics

An army vehicle of mass $1000\, kg$ is moving with a velocity of $10 \,m/s$ and is acted upon by a forward force of $1000\, N$ due to the engine and a retarding force of $500 \,N$ due to friction. ……….. $m/s$ will be its velocity after $10\, s$

medium

A body of mass $4 \mathrm{~kg}$ experiences two forces $\overrightarrow{\mathrm{F}}_1=5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{F}}_2=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$. The acceleration acting on the body is :

medium

(JEE MAIN-2024)

Write Newton’s second law of motion.

medium

The graph below shows the variation of a force $F$ with time $t$ on a body which is moving in a straight line. Dependence of force on time is $F \propto t^{n}$. Initially body is at rest. If the speed of the object is $2 \,m / s$ at $3 \,s$, then the speed at $4 \,s$ will be approximately (in $m / s$ )

normal

(KVPY-2018)

The velocity of a body of mass $2 \,kg $ as a function of $t$ is given by $\vec v (t)\, = \,2t\,\hat i\, + \,{t^2}\hat j\,$. Find the momentum and the force acting on it, at time $t = 2\,\sec $.

medium

Solution

Similar Questions

An army vehicle of mass $1000\, kg$ is moving with a velocity of $10 \,m/s$ and is acted upon by a forward force of $1000\, N$ due to the engine and a retarding force of $500 \,N$ due to friction. ……….. $m/s$ will be its velocity after $10\, s$

A body of mass $4 \mathrm{~kg}$ experiences two forces $\overrightarrow{\mathrm{F}}_1=5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{F}}_2=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$. The acceleration acting on the body is :

Write Newton’s second law of motion.

The velocity of a body of mass $2 \,kg $ as a function of $t$ is given by $\vec v (t)\, = \,2t\,\hat i\, + \,{t^2}\hat j\,$. Find the momentum and the force acting on it, at time $t = 2\,\sec $.

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