A particle is moving along a straight line parallel to x-axis with constant velocity. Its angular momentum about the origin

Options

A. decreases with time
B. increases with time
C. remains constant
D. is zero

Answer

C

Explanation

Suppose the particles of mass m is moving with speed v parallel to x axis as shown in figure , then at any time t , coordinates of P will be
`x = vt , y = b ` and z = 0
while components of velocity will be `v_(x)= v , v_(y) = 0 ` and `v_(z) = 0`
(as it is moving parallel to x-axis)

So , `vecL`
So , `vecL = vecr xx vecp = m |{:(hati , hatj , hatk) , (vt , b , 0), (v , 0 ,0):}| = hatk m[vt xx 0 - vb] = -mvb hatk`
i.e., angular momentum has magnitude mvb and is directed along negative z-axis i.e., angular momentum remains constant .