Question

A particle parallel to x-axis as shown in the figure such that at all instant the y axis component of its position vector is constant and is equal to b. The angular velocity of the particle about the origin is

• A. $v/b$
• B. $\left(v/b\right)Sin\theta$
• C. $\left(v/b\right)Si{n}^2\theta$
• D. $vb$

Answer 1

Answer: (C)

$\left(v/b\right)Si{n}^2\theta$

Let v1 and r1 are initial velocity and position respectively and v2 and r2 are final ones.

$m{v}_1{r}_1=m{v}_2{r}_2$

$v_1=v,r_1=b,r_2=b/sin\theta ,v_2=?,\omega =v_2/r_2$

$v_2=v_1{r}_1/r_2=vb/\left(b/sin\theta \right)=vsin\theta$

$\omega =vsin\theta /\left(b/sin\theta \right)$

$\omega =v/b\left(si{n}^2\theta \right)$