Aspherical steel ball bearing has a diameter of 2.540 cm at 20.00°c. (assume the coefficient of linear expansion for steel is 11 ✕ 10−6 (°c)−1. ) (a) what is its diameter when its temperature is raised to 87.0°c? (give your answer to at least four significant figures.) 2.542 correct: your answer is correct. cm (b) what temperature change is required to increase its volume by 0.900%

(a) 2.542 cm

(b) 272.7°C

Explanation:

diameter, d = 2.540 cm

T1 = 20°C

α = 11 x 10^-6 /°C

(a) Let d' be the diameter.

T2 = 87°C

Use he formula for the areal expansion

A' = A ( 1 + βΔT)

where, β is the coefficient of areal expansion and ΔT is teh rise in temperature, A' be the area at high temperature and A be the area at low temperature.

β = 2 α = 2 x 11 x 106-6 = 22 x 10^-6 /°C

So,

D'^2 = 2.54^2 ( 1 + 22 x 10^-6 x 67)

D' = 2.542 cm

(b) Let the change in temperature is ΔT.

Use the formula for the volumetric expansion

ΔV = V x γ x ΔT

Where, γ = 3 x α = 3 x 11 x 10^-6 = 33 x 10^-6 /°C

0.9/100 = 33 x 10^-6 x ΔT

ΔT = 272.7°C

c. magnitude and direction

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.