A mass M hangs on a massless rod of length l | vedclass

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

Question

(D) The angular momentum is defined as $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$.For point $A$ (the center of the circle): The po

Vedclass · Accepted Answer

$L_A$ is constant,both in magnitude and direction.

Vedclass · Answer

(D) The angular momentum is defined as $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$.For point $A$ (the center of the circle): The position vector $\vec{r}_A$ is in the plane of the circle,and the velocity vector $\vec{v}$ is tangent to the circle. The cross product $\vec{r}_A 	imes \vec{v}$ always points along the axis of rotation (the $z$-axis). Since the speed $v$ and radius $r$ are constant,the magnitude $L_A = mvr$ is constant,and the direction is fixed along the $+z$-axis. Thus,$L_A$ is constant.For point $B$ (the pivot point): The position vector $\vec{r}_B$ from $B$ to $M$ changes its direction as the mass rotates. Although the magnitude of the angular momentum $L_B$ remains constant,its direction changes continuously as the rod sweeps out a cone. Therefore,$L_B$ is not constant in direction.Comparing the options,the statement that $L_A$ is constant in both magnitude and direction is correct.

Similar Questions

The solution of the differential equation $\frac{dy}{dx} = \frac{y}{x} + \frac{\phi(y/x)}{\phi'(y/x)}$ is

Let a random variable $X$ have a binomial distribution with mean $8$ and variance $4$. If $P(X \le 2) = \frac{k}{2^{16}}$,then $k$ is equal to

The compound$(s)$ with $P - H$ bond$(s)$ is$(are)$
$(A) \ H _3 PO _4$ $(B) \ H _3 PO _3$ $(C) \ H _4 P _2 O _7$ $(D) \ H _3 PO _2$

Three students $A, B$,and $C$ are given a mathematics problem. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Vedclass Test Series

Exam Paper Generator

Online Exam Module