A block of mass m lies on wedge of mass M, which lies on fixed horizontal surface. The wedge is free to move on the horizontal surface. A horizontal force of magnitude F is applied on block as shown, neglecting friction at all surfaces, the value of force F such that block has no relative motion w.r.t. wedge will be: (where g is acceleration due to gravity)

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

$(M + m) g \tan θ$

$(M + m) g \cot θ$

$\frac{m}{M} (M + m) g \tan θ$

$\frac{m}{M} (M + m) g \cot θ$

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

For no relative motion between wedge and block, let the acceleration of both block and wedge be 'a' towards left.

From FBD of block; $N \cos θ = m g$ ...(i)
and $F - N \sin θ = m a$ ...(ii)
From FBD of wedge; $N \sin θ = M a$ ...(iii)
from equations (i), (ii) and (iii)

solving we get $F = \frac{m}{M} (M + m) g \tan θ$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th