Question

a) grams, c) meters, seconds, kilograms 6. A square piece of aluminium with as mass of 5.4 g has a length of 2 cm and a thickness \p= of 5 mm. What is the density of the piece of aluminiurn in miodbiM 7. A ball is thrown into the air with a velocity of 8m/s from on top of a 36m buil ding. How long does it take the ball to hit the ground? 8. The velocity of a particle is y(t) = (A-21) m/s i + (6t + 2) m/s j What is the speed of the particle at t = 3s?

Answer 1

(6) Mass of the aluminium piece, m = 5.4 g = 5.4 x 10^-3 kg

Volume of the aluminium piece, v = length x breadth x thickness

= 0.02 x 0.02 x 0.005 m^3 = 0.000002 m^3

Hence, density of aluminium piece, $\rho$ = m/v = (5.4 x 10^-3) / 0.000002 = 2700 kg/m^3

(7) The ball is thrown upward with a velocity, v = 8 m/s

Height of the building, h = -36 m (we have taken negative sign because we are taking the point of throwing as origin)

Use the expression -

h = v*t + (1/2)*g*t^2

=> -36 = 8t + 0.5*(-9.8)*t^2

=> 4.9t^2 - 8t - 36 = 0

=> t = [8 + sqrt(8^2 + 4*4.9*36)] / (2*4.9)

= [8 + 27.7] / 9.8 = 3.64 s (Answer)

Other value of 't' can be discarded as it will be negative.

(8) At, t = 3 s

v(3) = (3^2 - 2*3)m/s i + (6*3 + 2) m/s j = 3 m/s i + 20 m/s j

So, magnitude of velocity, |v| = sqrt[3^2 + 20^2] = 20.22 m/s (Answer)