Circular MotionHard
Question
A small block slides with velocity 0.5 
on the horizontal frictionless surface as shown in the Figure. The block leaves the surface at point C. The angle θ in the Figure is :
on the horizontal frictionless surface as shown in the Figure. The block leaves the surface at point C. The angle θ in the Figure is :Options
A.cos-1 (4/9)
B.cos-1 (3/4)
C.cos-1 (1/2)
D.none of the above
Solution
Given vB = 0.5 
Assume block leave the contact at C, N = 0
= mg cos θ .... (1)
from energy conservation
mvB2 + mgr (1 − cos θ) = 
mvC2 ........... (2)
from equation (1) and (2).
m 
+ mg r (1 − cos θ) = 
mg r cos θ
⇒ cos θ =
⇒ θ = cos-1 Ans.
Assume block leave the contact at C, N = 0
= mg cos θ .... (1)from energy conservation
mvB2 + mgr (1 − cos θ) = mvC2 ........... (2)from equation (1) and (2).
m + mg r (1 − cos θ) = mg r cos θ⇒ cos θ =
⇒ θ = cos-1
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