Question 108: Laws of Motion

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 = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

Accepted Answer

Let acceleration of wedge is a
w
and acceleration of block w.r.t. wedge is a
b
For the wedge w.r.t. ground
N cos60$$^\circ$$ = Ma
w
= 16a
w
$$\Rightarrow$$ N = 32a
w
F.B.D. of block w.r.t. wedge
Balancing vertical forces
N = 8g cos30$$^\circ$$ $$-$$ 8a
w
sin30$$^\circ$$ $$\Rightarrow$$ 32a
w
= 4$$\sqrt 3 $$g $$-$$ 4a
w
$$\Rightarrow$$ a
w
= $${{\sqrt 3 } \over 9}$$g
Along incline plane
8g sin30$$^\circ$$ + 8a
w
cos30$$^\circ$$ = ma
b
= 8a
b
a
b
= g $$	imes$$ $${1 \over 2} + {{\sqrt 3 } \over 9}$$g . $${{\sqrt 3 } \over 2} = {{2g} \over 3}$$
Option (d)

Answer

$${4 \over 3}g$$

Answer

$${6 \over 5}g$$

Answer

$${3 \over 5}g$$

Answer

$${2 \over 3}g$$

Laws of Motion

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 = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

Choose the correct answer: