Question

Two blocks A and B are released on the inclined plane of angle 30° and a circular track of radius R from different height h1
and h2 respectively. The mass of each block is m. If F1 and F2 are the respective forces experienced by two blocks at the
bottom-most point of the tracks and F1 = F2, then find the value of h2 (in m) for R = 8 m.
Options:1,2,3,4,5,6,7,8,9,0
Can anyone EXPLAIN this answer please?? I need it now ​

Answer 1

Given : Block of mass m

           height of the iinclined plane = h₁

           radius of circular track = 8 m

            F₁ = F₂

The force experienced by the block after reaching at the bottom

F₁ = ma

During this the potential energy of block is converted in to the kinetic energy

PE = mgh₁

⇒ KE = mgh₁

⇒ 1/2 mv² = mgh₁

⇒ v² = 2gh₁

we know the block has started from rest ⇒ u = 0

also it has travelled a distance of s = h₁/sin 30°

We have,

v² - u² = 2as

⇒ 2gh₁ - 0 = 2 a h₁/sin 30°

⇒ a = g/2 m/s²

∴ F₁ = ma = mg/2

when the block moves in circular track its potential energy is converted in to kinetic energy at the bottom

PE = mgh₂

⇒ KE = mgh₂

⇒ 1/2 mv² = mgh₂

⇒ v² = 2gh₂

The force experienced at the bottom of the circular track

F₂ = mg + mv²/R    (∵ centripetal force)  

⇒ F₂ = mg + m 2gh₂/8

⇒ F₂ = mg + mgh₂/4

∵ F₁ = F₂

⇒ mg/2 = mg + mgh₂/4

⇒ h₂/4 = -1/2

  ∴ h₂ = -2 m

HOPE THIS HELPS YOU !!   : )