Question

A 1.00-kg object A is connected with a massless string across a massless, frictionless pulley to a 2.00-kg object B. The smaller object rests on an inclined plane which is tilted at an angle of θ= 30.0°
a. What is the acceleration of the system? (Express your answer to three significant figures.)
b. What is the tension in the string? (Express your answer to three significant figures.)

Answer 1

Tension of the object is = 12.25

Acceleration of the system= 7.35 m/s²

Explanation:

Given

mass of A= 1kg

mass of B= 2kg

angle = 30°

let us consider the second mass m₂ of object B

m₂g - T = m₂a

T + 2a= 2 × 9.8

T + 2a=  19.6

where T denotes the tension of the cord and "a" being the acceleration.

Now considering mass m₁ of object A

T - m₁gsin θ  = m₁a

T - (9.8 × sin30°) = a

T - a = 4.9

on solving the above equations we get,

T + 2a = 19.6

T - a = 4.9

The tension T of the object is = 12.25

Acceleration a of the system= 7.35 m/s²