Questionmb A block of mass 3 m can move without friction on a horizontal table. This block is attached to another block of mass $m$ by a cord that passes over a frictionless pulley, as shown above. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block? (A) $g / 4$ (B) $g / 3$ (C) $2 g / 3$ (D) g

Studdy Solution
Solve the system of equations to find the acceleration.
First, solve the equation for the block of mass $3m$ for $T$: $T = 3m \cdot a$
Substitute $T = 3m \cdot a$ into the equation for the descending block: $m \cdot a = mg - 3m \cdot a$
Combine like terms: $m \cdot a + 3m \cdot a = mg$ $4m \cdot a = mg$
Divide both sides by $4m$ to solve for $a$: $a = \frac{mg}{4m}$ $a = \frac{g}{4}$
The magnitude of the acceleration of the descending block is:
$\boxed{\frac{g}{4}}$