In the figure acceleration of A is 1 m / s 2 upwards, acceleration of B is 7 m / s 2 upwards and acceleration of C is 2 m / s 2 upwards. The acceleration of D will be

Question

In the figure acceleration of A is 1 m / s 2 upwards, acceleration of B is 7 m / s 2 upwards and acceleration of C is 2 m / s 2 upwards. The acceleration of D will be (A) 7 m / s 2 downwards (B) 2 m / s 2 downwards (C) 10 m / s 2 downwards (D) 8 m / s 2 downwards

Tardigrade Admin · Accepted Answer

Acceleration of pulley P aP=(aA+aB/2)=(1+7/2)=4 m / s 2 (upward) Acceleration pulley Q will be 4 m / s 2 downwards. aQ=(aD-aC/2) 4=(aD-2/2) ⇒ aD=10 m / s 2( downarrow)

Q. In the figure acceleration of $A$ is $1 m / s^{2}$ upwards, acceleration of $B$ is $7 m / s^{2}$ upwards and acceleration of $C$ is $2 m / s^{2}$ upwards. The acceleration of $D$ will be

$7 m / s^{2}$ downwards

$2 m / s^{2}$ downwards

$10 m / s^{2}$ downwards

$8 m / s^{2}$ downwards

Acceleration of pulley $P$
$a_{P} = \frac{a _{A} + a _{B}}{2} = \frac{1 + 7}{2} = 4 m / s^{2}$ (upward)
Acceleration pulley $Q$ will be $4 m / s^{2}$ downwards.
$a_{Q} = \frac{a _{D} - a _{C}}{2}$
$4 = \frac{a _{D} - 2}{2}$
$\Rightarrow a_{D} = 10 m / s^{2} (↓)$

Q. In the figure acceleration of A is 1m/s2 upwards, acceleration of B is 7m/s2 upwards and acceleration of C is 2m/s2 upwards. The acceleration of D will be

7m/s2 downwards

2m/s2 downwards

10m/s2 downwards

8m/s2 downwards