A frictionless track A B C D E ends in a circular loop of radius R. A body slides down the track from point A which is at a height h = 5 cm . Maximum value of R for the body to successfully complete the loop is

Question

A frictionless track A B C D E ends in a circular loop of radius R. A body slides down the track from point A which is at a height h = 5 cm . Maximum value of R for the body to successfully complete the loop is (A) 5 cm  (B) (15/4) cm (C) (10/3) cm (D) 2 cm

Tardigrade Admin · Accepted Answer

Potential energy of the body at point A = kinetic energy of the body at point B m g h=(1/2) m v2 g h=(v2/2) Velocity at lowest point in a vertical circle v=√5 R g g h=(5 R g/2) R=(2 h/5) But h=5 cm ∴ R=(2 × 5/5)=2 cm

Q. A frictionless track $A BC D E$ ends in a circular loop of radius $R . A$ body slides down the track from point $A$ which is at a height $h = 5 c m$ . Maximum value of $R$ for the body to successfully complete the loop is

$5 c m$

$\frac{15}{4} c m$

$\frac{10}{3} c m$

$2 c m$

Potential energy of the body at point $A$
$=$ kinetic energy of the body at point $B$
$m g h = \frac{1}{2} m v^{2}$
$g h = \frac{v ^{2}}{2}$
Velocity at lowest point in a vertical circle
$v = 5 R g$
$g h = \frac{5 R g}{2}$
$R = \frac{2 h}{5}$
But $h = 5 c m$
$∴ R = \frac{2 \times 5}{5} = 2 c m$

Q. A frictionless track ABCDE ends in a circular loop of radius R.A body slides down the track from point A which is at a height h=5cm . Maximum value of R for the body to successfully complete the loop is

5cm

415​cm

310​cm

2cm