Question

A shell acquires the initial velocity $v$ = 320 m/s, having made $n$ = 2.0 turns inside the barrel whose length is equal to $l$ = 2.0 m. Assuming that the shell moves inside the barrel with a uniform acceleration, find the angular velocity of its axial rotation at the moment when the shell escapes the barrel.

• A. $20\frac{rad}{sec}$
• B. $200\frac{rad}{sec}$
• C. $2010\frac{rad}{sec}$
• D. Data insufficient

Answer 1

The correct option is C

$2010\frac{rad}{sec}$

When the shell comes out if acquires the velocity of 320 m/s.

$\Rightarrow u=0$

$v=320$

$s=2m$

$\Rightarrow v^2=u^2+2as$

$(320{)}^2=2.a.2$

$\Rightarrow a=(160{)}^2$

$V=u+at$

$320=(160{)}^{2}t$

$t=\left(\frac{1}{80}\right)sec$

Now in this time the shell has rotated twice.

This means each and every point would have made one angular displacement of

$\theta =4\pi$

${\omega }_0=0$

$t=\frac{1}{80}$

$\theta ={\omega }_{0}t+\frac{1}{2}a{t}^2$

$\Rightarrow 4\pi =\frac{1}{2}a(\frac{1}{80}{)}^2$

$a=8\pi \times (80{)}^2$

${\omega }_t={\omega }_0+at$

$\Rightarrow {\omega }_t=8\pi \times (80{)}^2\times \frac{1}{80}$

$=640\pi$

$\omega =2010\frac{rad}{sec}$