Resolve a weight of 10 N in two directions which are parallel and perpendicular to a slope inclined at 30o to the horizontal.

Question

Resolve a weight of 10 N in two directions which are parallel and perpendicular to a slope inclined at 30o to the horizontal. (A)  w⊥ =5√3N, w||=5N  (B)  w⊥ =5N, w||=5√3N  (C)  w⊥ =5√3, w||=0N  (D)  w⊥ =0N, w||=5N

Tardigrade Admin · Accepted Answer

Component perpendicular to the plane w⊥ =w cos 30o =10× (√3/2) =5√3N and component parallel to the plane w||=w sin 30o =10× (1/2) = 5 N

Q. Resolve a weight of $10 N$ in two directions which are parallel and perpendicular to a slope inclined at $30^{o}$ to the horizontal.

$w_{⊥} = 53 N, w_{∣∣} = 5 N$

$w_{⊥} = 5 N, w_{∣∣} = 53 N$

$w_{⊥} = 53, w_{∣∣} = 0 N$

$w_{⊥} = 0 N, w_{∣∣} = 5 N$

Component perpendicular to the plane
$w_{⊥} = w cos 30^{o}$
$= 10 \times \frac{3}{2}$
$= 53 N$
and component parallel to the plane
$w_{∣∣} = w sin 30^{o}$
$= 10 \times \frac{1}{2} = 5 N$

Q. Resolve a weight of 10N in two directions which are parallel and perpendicular to a slope inclined at 30o to the horizontal.

w⊥​=53​N,w∣∣​=5N

w⊥​=5N,w∣∣​=53​N

w⊥​=53​,w∣∣​=0N

w⊥​=0N,w∣∣​=5N