Question

A body is projected from ground with some angle to the horizontal. The angular momentum about the initial position will(a) decrease(b) increase(c) remains same(d) first increase then decrease

Answer 1

answer

explanation : A body is projected with speed u m/s from ground at an angle $\theta$ with horizontal.

then, velocity of body at time t,

$\vec{v}=ucos\theta\hat{i}+(usin\theta-gt)\hat{j}$

position of particle at time t,

$\vec{x}=(ucos\theta t)\hat{i}+\left(usin\theta t-\frac{1}{2}gt^2\right)\hat{j}$

so, angular momentum of particle at time t, $\vec{L}=m(\vec{x}\times\vec{v})$

= $m[(usin\theta.cos\theta t-ucos\theta gt^2)\hat{k}-(usin\theta.cos\theta t-0.5ucos\theta gt^2)\hat{k}]$

= $-\frac{1}{2}mucos\theta gt^2\hat{k}$

here , $\theta$, m and g are constant terms . so, it is clear that, angular momentum depends on time.

hence, it increases when increase time. [negative sign just show direction of angular momentum]

hence, option (b) is correct.

Answer 2

Answer:

Increases

Explanation: