Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5

Q.

A bead slides without friction around a loop-the-loop (Fig.). The bead is released from rest at a height h = 3.50R. How large is the normal force on the bead at point (A) if its mass is 50 g?

 

Question Image

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

0.10 N downward

b

0.10 N upward

c

1.0 N downward

d

1.0 N upward

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

detailed_solution_thumbnail

The speed at the top can be found from the conservation of energy for the bead-track-Earth system,
We define the bottom of the loop as the zero level for the gravitational potential energy.

Since vi = 0, Ei = Ki+Ui = 0 + mgh = mg(3.50R)

The. total energy of the bead at point (A) can be written as EA = KA+UA = 12mvA2+mg(2R)

Since mechanical energy is conserved, Ei = EA, we get

mg(3.50R) = 12mvA2+mg(2R)

simpliflying, vA2 = 3.0 gR  vA = 3.0 gR

To find the normal force at the top, we construct a force diagram as shown,

Question Image

Here we assume that N is downward, like mg.

 Fy = may; N + mg = mv2r

N = m[v2R-g] = m[3.0gRR-g] = 2.0 mg

N = 2.0(50×10-3kg)(10.0 m/s2)

   = 1.0 N downward

Watch 3-min video & get full concept clarity

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon