Math  /  Algebra

Questionmb A block of mass 3 m can move without friction on a horizontal table. This block is attached to another block of mass mm 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/4g / 4 (B) g/3g / 3 (C) 2g/32 g / 3 (D) g

Studdy Solution
Solve the system of equations to find the acceleration.
First, solve the equation for the block of mass 3m3m for TT: T=3maT = 3m \cdot a
Substitute T=3maT = 3m \cdot a into the equation for the descending block: ma=mg3mam \cdot a = mg - 3m \cdot a
Combine like terms: ma+3ma=mgm \cdot a + 3m \cdot a = mg 4ma=mg4m \cdot a = mg
Divide both sides by 4m4m to solve for aa: a=mg4ma = \frac{mg}{4m} a=g4a = \frac{g}{4}
The magnitude of the acceleration of the descending block is:
g4 \boxed{\frac{g}{4}}

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