A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( g= gravitational acceleration)

Question

A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( g= gravitational acceleration) (A) g (B) 3 g (C) 4 g (D) 6 g

Tardigrade Admin · Accepted Answer

Critical velocity at top most point v = √r g ∴ Velocity when string become horizontal v ' = √ upsilon2 + 2 g r = √3 g r Centripetal acceleration = ( upsilon2/r) = (3 r g/r) = 3 g

Q. A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( $g =$ gravitational acceleration)

$g$

3 $g$

4 $g$

6 $g$

Critical velocity at top most point $v = r g$
$∴$ Velocity when string become horizontal
$v^{'} = υ^{2} + 2 g r$
$= 3 g r$
Centripetal acceleration $= \frac{υ ^{2}}{r} = \frac{3 r g}{r} = 3 g$

Q. A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( g= gravitational acceleration)

g

3 g

4 g

6 g

Critical velocity at top most point v=rg​ ∴ Velocity when string become horizontal v′=υ2+2gr​ =3gr​ Centripetal acceleration =rυ2​=r3rg​=3g

Q. A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( $g =$ gravitational acceleration)

$g$

3 $g$

4 $g$

6 $g$

Critical velocity at top most point $v = r g$
$∴$ Velocity when string become horizontal
$v^{'} = υ^{2} + 2 g r$
$= 3 g r$
Centripetal acceleration $= \frac{υ ^{2}}{r} = \frac{3 r g}{r} = 3 g$