Question

a block of mass m slides on the wooden wedge which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: 
[ Given m= 8kg, M=16kg ]
[Assume all the surfaces shown in the figure to be frictionless] 
 

• A. \(\frac{4}{3}g\)
• B. \(\frac{6}{5}g\)
• C. \(\frac{3}{5}g\)
• D. \(\frac{2}{3}g\)

Answer 1

The Correct Option is D

The correct answer is (D) : \(\frac{2g}{3}\)
N cos60∘ = Ma₁​ = 16a₁​⇒ N = 32a₁​​⊥ to incline N = 8g cos30^∘ − 8a₁ ​sin30^∘ ⇒ 32
a_1​ = 4√3​g − 4a₁
A₂ = \(\frac{\sqrt3}{9}\)g
​8g sin30^∘ + 8a₁​ cos30^∘ = ma₂ ​= 8a₂
a₂ = g\(\times\)\(\frac{1}{2}\)\(\times\)\(\frac{\sqrt3}{9}\)g\(\times\)\(\frac{\sqrt3}{2}\)
= \(\frac{2g}{3}\)