In the situation as shown in figure if acceleration of B is a then find the acceleration of A (B always remains horizontal)

Question

In the situation as shown in figure if acceleration of B is a then find the acceleration of A (B always remains horizontal) (A) a sin θ (B) a cot θ (C) 2 a tan θ (D) 2 a cos θ

Tardigrade Admin · Accepted Answer

Components of accelerations of A and B along normal ( hatn) to the incline of wedge should be same. ⇒ A sin θ=a cos (2 θ-90°) ⇒ A sin θ=a sin 2 θ ⇒ A=2 a cos θ

Q. In the situation as shown in figure if acceleration of $B$ is a then find the acceleration of $A$ ( $B$ always remains horizontal)

$a sin θ$

$a cot θ$

$2 a tan θ$

$2 a cos θ$

Components of accelerations of $A$ and $B$ along normal $(\overset{n}{^})$ to the incline of wedge should be same.
$\Rightarrow A sin θ = a cos (2 θ - 9 0^{\circ})$
$\Rightarrow A sin θ = a sin 2 θ$
$\Rightarrow A = 2 a cos θ$

Q. In the situation as shown in figure if acceleration of B is a then find the acceleration of A (B always remains horizontal)

asinθ

acotθ

2atanθ

2acosθ