ABCDE is a channel in vertical plane, part BCDE being circular with radius r . A block is released f

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5.Work, Energy, Power and Collision

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$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

$h \leq \frac{3}{2}r$

$h \geq \frac{5}{2}r$

$h \geq \frac{3}{2}r$

$h \leq \frac{5}{2}r$

Solution

Loss in $PE$ between $A$ and $D=$ gain in $KE$ between $A$ and $D$

${\mathop{\rm mg}\nolimits} ({\rm{h}} – 2{\rm{r}}) = \frac{1}{2}{\rm{m}}\left( {{{\rm{v}}^2} – 0} \right)\quad \left( {{{\rm{K}}_{\rm{A}}} = 0} \right)$

$\mathrm{v}^{2} =2 \mathrm{g}(\mathrm{h}-2 \mathrm{r})$ …..$(i)$

If the block is to complete the loop path then at $D$

$\frac{\mathrm{mv}^{2}}{\mathrm{r}} \geq \mathrm{mg}$

$\mathrm{v}^{2} \geq \mathrm{rg}$ …..$(ii)$

From Eqs. $(i)$ and $(ii)$

$2g(h – 2r) \ge rg$

$h \geq \frac{5}{2} r$

Standard 11

Physics

A frictionless track $ABCDE$ ends in a circular loop of radius $R$ .A body slides down the track from point $A$ which is at a height $h = 5\, cm$. Maximum value of $R$ for the body to successfully complete the loop is ……………… $\mathrm{cm}$

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State if each of the following statements is true or false. Give reasons for your answer.

$(a)$ In an elastic collision of two bodies, the momentum and energy of each body is conserved.

$(b)$ Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.

$(d)$ In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

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$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

Solution

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