(B) Let the rod have length $L$. The coordinates of ends $A$ and $B$ are $(0, y)$ and $(x, 0)$ respectively.Since the rod is rigid,$x^2 + y^2 = L^2$.D

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(B) Let the rod have length $L$. The coordinates of ends $A$ and $B$ are $(0, y)$ and $(x, 0)$ respectively.Since the rod is rigid,$x^2 + y^2 = L^2$.Differentiating with respect to time $t$,we get $2x(dx/dt) + 2y(dy/dt) = 0$.Here,$dy/dt = -u$ (as $y$ is decreasing) and $dx/dt = v$ (velocity of end $B$).So,$xv + y(-u) = 0$,which gives $xv = yu$.From the geometry,$x = L \cos \theta$ and $y = L \sin \theta$.Substituting these,$(L \cos \theta)v = (L \sin \theta)u$.Therefore,$v = u \frac{\sin \theta}{\cos \theta} = u \tan \theta$.

Class 11 Physics Newton's Laws of Motion and Friction Constrained Motion

Medium

The velocity of end $A$ of a rigid rod placed between two smooth perpendicular walls moves with velocity $u$ along the vertical direction. Find the velocity of end $B$ of the rod,given that the rod always remains in contact with the walls.

A
$u \tan 2\theta$
B
$u \tan \theta$
C
$u \cot \theta$
D
$2u \tan \theta$

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Newton's Laws of Motion and Friction

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Constrained Motion

Two equal masses $A$ and $B$ are arranged as shown in the figure. The pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is:

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The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys as shown in the figure. Calculate the time taken by the box of mass $8\, {kg}$ to strike the ground starting from rest. (Use $g = 10\, {m/s^2}$) (in ${s}$)

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Calculate the acceleration of the block $B$ in the figure,assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and the pulleys and string are massless.

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The pulleys in the diagram are all smooth and light. The acceleration of $A$ is $a$ upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ is

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In the arrangement shown in the figure,$a_{1}, a_{2}, a_{3}$ and $a_{4}$ are the accelerations of masses $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively. Which of the following relations is true for this arrangement?

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The velocity of end $A$ of a rigid rod placed between two smooth perpendicular walls moves with velocity $u$ along the vertical direction. Find the velocity of end $B$ of the rod,given that the rod always remains in contact with the walls.

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Two equal masses $A$ and $B$ are arranged as shown in the figure. The pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is:

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys as shown in the figure. Calculate the time taken by the box of mass $8\, {kg}$ to strike the ground starting from rest. (Use $g = 10\, {m/s^2}$) (in ${s}$)

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