Question

Find the force exerted by spring on the wedge shown in the figure. Assume that mass $\text{M}$ is in equilibrium (all surfaces are smooth).Take $g=10{\text{m/s}}^2$.

• A. $18\text{N}$
• B. $12\text{N}$
• C. $36\text{N}$
• D. $24\text{N}$

Answer 1

The correct option is D $24\text{N}$

From FBD of wedge


Applying equilibrium condition for wedge in horizontal direction:

$N\cos {53}^{\circ }=kx$ ......(i)

$\because$ Block's acceleration $\perp$ to inclined plane $=0$, equating forces acting on block (perpendicular to the inclined plane)

$N=mg\cos {37}^{\circ }$ .......(ii)
Putting (ii) in (i)

$kx=mg\cos {37}^{\circ }.\cos {53}^{\circ }$

$kx=5\times 10\times 0.8\times 0.6$
$kx=24N$
Hence spring force $=kx=24\text{N}$