A rod of length L leans against a smooth vert | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the position of the upper end be $(0, y)$ and the lower end be $(x, 0)$. Since the rod has a fixed length $L$, we have $x^2 + y^2 = L^2$.Diffe

Vedclass · Accepted Answer

The speed of the lower end gets smaller and smaller and vanishes when the upper end touches the ground.

Vedclass · Answer

(C) Let the position of the upper end be $(0, y)$ and the lower end be $(x, 0)$. Since the rod has a fixed length $L$, we have $x^2 + y^2 = L^2$.Differentiating with respect to time $t$, we get $2x(dx/dt) + 2y(dy/dt) = 0$.Let the velocity of the upper end be $v = -dy/dt$ (downward) and the velocity of the lower end be $v' = dx/dt$ (rightward).Substituting these, we get $x v' - y v = 0$, which implies $v' = v(y/x)$.Since $y/x = 	an 	heta$, where $	heta$ is the angle the rod makes with the floor, we have $v' = v 	an 	heta$.As the upper end moves downward, the angle $	heta$ decreases. As $	heta 	o 0$, $	an 	heta 	o 0$, and consequently $v' 	o 0$.Thus, the speed of the lower end decreases and vanishes when the upper end touches the ground.

$A$ rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative.

Similar Questions

If $m_1 = 4m_2$,what is the acceleration of $m_2$? The acceleration of $m_1$ is $a$.

If the blocks $A$ and $B$ are moving towards each other with accelerations $a$ and $b$ respectively,find the net acceleration of block $C$.

Consider the situation shown in the figure. All the surfaces are smooth. The tension in the string connected to $2m$ is

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?

Block $B$ moves to the right with a constant velocity $v_0$. The velocity of body $A$ relative to $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module