Question

A particle of mass m is moving with a uniform speed v in x-y plane along the straight line y=x+k , the angular momentum of the particle about the origin is

Answer 1

Answer:

Given:

Mass = m

Equation of line along which the particle travels : y = x + k

To find:

Angular momentum of the body with respect to origin (0,0)

Concept:

First you need to find the perpendicular distance from origin to that line .

For a equation : Ax + By + C = 0

The perpendicular distance from (x1,y1) is given by the following formula

D = | Ax1 + By1 + C | /(A² + B²)

Calculation:

In this case:

D = [(1×0) - (1×0) - k]/(1² +1²)

=> D = k/(√2) ............(a)

Now angular momentum

= m × v × (d⊥)

= m × v × D

= mv (k/√2)

So , the actual answer is

$L \: = \frac{mvk}{ \sqrt{2} }$

Answer 2

Answer:

L=mvk/√2

Explanation:

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