Question

28
the ball can
in
A some verlede angle of the conical section
oko tunnel
37. There is
a
small ball kept inside the
funnel on rocating the funnel the
maxóum speed theca
chave
order to remain in the
fund u 2m/s . caluate the
inner radius of the deirin of
the lunnd it there any dimit
lepon U ration!
How much at ago Is it down
epper
logical
team than gelom isto
limit? give
a logical reason? (use g=10m/s)​

Answer 1

Answer:

nxksksmnsksmsmsnnsmskskkskskksksksk

Answer 2

▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄

Correct Question

semi - vertical angle of the conical section of a funnel is 37°.There is a small ball kept inside the funnel.on rotating the funnel,the maximum speed that the ball can have in order to remain in the funnel is 2 m/s.Calculate the inner radius of the brim of the funnel.Is there any limit upon the frequency oh rotation?How much is it ?It is lower or upper limit ?Give a logical reasoning.(Use g = 10 m/s² and and sin 37° = 0.6)

Solution

N Sinθ = mg and N cosθ = mv²/r

∴tan θ = rg/v² .°. r = v² tanθ/g

∴ ${\sf{ \large{r}}}$${ \sf{ \small{max}}}$$\sf{ { = v}^{2}}$${ \sf{ \small{max}}}{ \sf{ \frac{tanθ}{g} = 0.3m}}$=v²max tanθ=0.3m

v = rw = 2π rn

If we go for the lowest limit of the speed(while rotating), v → 0 .°. r →0,but the frequency n increases.

Hence a specific upper limit is not possible in the case of frequency.

Thus,the Practical limit on the frequency of rotation is it lower limit.It will be possible for r = r^max

∴ n = n ^max /2πr ^max= 1/0.3π = 1 rev / s.

▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄