A rock is suspended from a scale reads 15.0 N. A beaker of water (having a densi

Question

A rock is suspended from a scale reads 15.0 N. A beaker of water (having a density of 1000 kg/m^3) is raised up so the rock is totally submerged in the water. The scale now reads 5 N. What is the buoyant force? _______ What is the density of the rock? _________ Water is flowing in a horizontal pipe of radius I m. Suppose you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new radius ? _______ The gravitational acceleration on the surface a planet you just discovered is 18.0 m/s^2. What is the gravitational acceleration at an altitude of one planet diameter above the SURFACE of the planet?______ Suppose you found a second planet where the gravitational acceleration on its surface is half that of the first planet (9 m/s^2). What is the ratio of the mass of the first planet to the second planet? _______ A 100-kg object is released from rest at an altitude of 2R above the north pole of the earth. If we ignore atmospheric friction, with what speed does the object strike the surface of the earth? Give your answer in terms of G, R and M_earth (the polar radius of the earth is R) _______ An object of mass 1.0 kg is attached to an ideal massless spring and allowed to hang in the Earth's gravitational field. The spring stretches 4 cm before it reaches its equilibrium position. If this system is allowed to oscillate. What is the spring constant ? _________ What will be its frequency? __________

Explanation / Answer

5)

A) buoyant force = 15-5 = 10 N

B) buoyant force = density of liquid*volume*9.8

So, 10 = 1000*V*9.8

So, V = 1.02*10^-3 m3

So, density of rock = (15/9.8)/(1.02*10^-3)

= 1500.6 kg/m3

6)

A1*v1 = A2*v2

So, (pi*1^2)*v = (pi*r^2)*(v/2)

So, r = sqrt(2) = 1.414 m

7)

A)

a = GM/R^2 = 18 m/s2

So, at a height of h = 2R

a' = GM/(R+2R)

= GM/3R = 18/3 = 6 m/s2

B)

g = GM/R^2

So, g/g' = M/M'

So, 18/9 = M/M' = 2

So, ratio of masses of 1st planet to 2nd = 2:1

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