SATHEE: Rotational Motion Question 30

Rotational Motion Question 30

Question: A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

[JEE MAIN 2013]

Options:

A) $\frac{r ω_{0}}{4}$

B) $\frac{r ω_{0}}{3}$

C) $\frac{r ω_{0}}{2}$

D) $r ω_{0}$

Show Answer

Answer:

Correct Answer: C

Solution:

$\frac{ω}{2}$

Radius of hoop = r, Initial angular velocity =ω0,

Initial velocity (u) = 0,

velocity of centre of hoop = ?

By momentum conservation, initial momentum of hoop will be same as final momentum

i.e., $L_{i} = L_{f}$

$m r^{2} ω 0 = m v r + \frac{m r^{2} v}{r}$ rω0 = v+v v= $\frac{r ω 0}{2}$

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Rotational Motion Question 30

Question: A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Options:

Answer:

Solution:

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