The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If θ is the angle of friction and θ is the angle which the plane makes with the horizontal, then :

Question

The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If θ is the angle of friction and θ is the angle which the plane makes with the horizontal, then : (A)  tan φ=2 tan θ (B)  tan φ=3 tan θ (C)  tan φ= tan θ (D)  tan θ=3 tan φ

Tardigrade Admin · Accepted Answer

Here, m g( sin φ+μ cos φ)=2 m g( sin φ-μ cos φ) ⇒ tan φ=3 μ As μ= tan θ So, tan φ=3 tan θ

Q. The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $θ$ is the angle of friction and $θ$ is the angle which the plane makes with the horizontal, then :

$tan ϕ = 2 tan θ$

$tan ϕ = 3 tan θ$

$tan ϕ = tan θ$

$tan θ = 3 tan ϕ$

Here, $m g (sin ϕ + μ cos ϕ) = 2 m g (sin ϕ - μ cos ϕ)$
$\Rightarrow$ $tan ϕ = 3 μ$
As $μ = tan θ$
So, $tan ϕ = 3 tan θ$

Q. The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If θ is the angle of friction and θ is the angle which the plane makes with the horizontal, then :

tanϕ=2tanθ

tanϕ=3tanθ

tanϕ=tanθ

tanθ=3tanϕ