A particle of mass m , initially at rest, is acted on by a force F = F_0 left{ {1 - {{left( {frac{{2

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4-1.Newton's Laws of Motion

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A particle of mass $m$, initially at rest, is acted on by a force $F = F_0 \left\{ {1 - {{\left( {\frac{{2t - T}}{T}} \right)}^2}} \right\}$ during the interval $0 \leq 0 \leq t \leq T$. The velocity of the particle at the end of the interval is :

A

$\frac{{5{F_0}T}}{{6m}}$

B

$\frac{{4{F_0}T}}{{3m}}$

C

$\frac{{2{F_0}T}}{{3m}}$

D

$\frac{{3{F_0}T}}{{2m}}$

Solution

Let us assume that,

The initially particle was at rest. By the application of forces its momentum increases.

Final momentum of the particle $=$ area of $F-t$ graph

$mv =$ Area of semicircle

$=\frac{\pi r_1 r_2}{2}$

$=\frac{\pi\left( F _0\right)\left(\frac{ T }{2}\right)}{2} v$

$=\frac{\pi F _0 T }{4 m }$

Standard 11

Physics

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