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.)

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