badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th pass

                        

A rod of mass m and length l is kept on a smooth wedge of mass M.if the system is released when the rod is at the top of the wedge ,find the speed of the wedge when the rod hits the ground level.(neglect friction between all surfaces in contact)

2 years ago

Answers : (1)

Arun
24742 Points
							
We can use conservation of energy to solve this... or by using forces (normal) between wedge M and the rod m.
Here on the system of rod m and wedge M, work is done only by the gravitational force on rod m.
The PE lost by the rod :   m g H
Wedge displaces horizontally by x. The rod displaces vertically by y.
=> y = x tanФ.        Differentiate wrt time, to get:
=> v1 = v2 tanФ
=> a1 = a2 tanФ
When the rod touches the ground, velocity of wedge = v2.
KE of Wedge = 1/2 M v2²
KE of the rod  = 1/2 m v1² = 1/2 m v2 tan²Ф
Using conservation of energy:  m g H = 1/2 v2² (M + m tan²Ф)
v2² = 2 m g H /(M + m tan²Ф)

===============
If we use the method of forces, then Normal reaction force N between the rod m and wedge M gives the acceleration to Wedge.
Draw the Free body diagram for wedge and the rod.
N SinФ = M a₂
m g - N CosФ = m a₁ = m a₂ tanФ
=>  m g - M a₂ CotФ = m a₂ TanФ
=>  a₂ = mg Tan Ф /(M+m tan²Ф )
Distance traveled by the wedge: H CotФ   (the base of wedge)
=>  v₂² = 2 a₂ H CotФ
 
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details