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Unformatted text preview: ouseph (jao888) – HW01 – tsoi – (92940) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A room is 16 . 7 ft deep, 23 . 3 ft wide and 7 . 37 ft high. Find the volume of this room. 1 inch = 2.54 cm. Correct answer: 81 . 2054 m 3 . Explanation: Let : ℓ = 16 . 7 ft , w = 23 . 3 ft , and h = 7 . 37 ft . The volume is V = ℓ w h = (16 . 7 ft)(23 . 3 ft)(7 . 37 ft) parenleftbigg 12 in ft parenrightbigg 3 × parenleftbigg 2 . 54 cm in parenrightbigg 3 parenleftBig m 100 cm parenrightBig 3 = 81 . 2054 m 3 . 002 10.0 points A newly discovered giant planet has an aver- age radius 17 times that of the Earth and a mass 312 times that of the Earth. Calculate the ratio of the new planet’s den- sity to the Earth’s density. Correct answer: 0 . 063505. Explanation: Let : R n = 17 R E and m n = 312 m E . A spherical planet of average radius R has volume 4 3 π R 3 , so the density is ρ = m v = m 4 3 π R 3 = 3 m 4 π R 3 ∝ m R 3 . For two planets of respective radii R N and R E and masses m N and m E we have ρ N ρ E = m N R 3 N m E R 3 E = parenleftbigg m N m E parenrightbigg parenleftbigg R N R E parenrightbigg 3 = 312 (17) 3 = . 063505 . 003 (part 1 of 2) 10.0 points This problem shows how dimensional analysis helps us check and sometimes even find a formula. A rope has a cross section A = 10 . 5 m 2 and density ρ = 1900 kg / m 3 . The “linear” density of the rope μ , defined to be the mass per unit length, can be written in the form μ = ρ x A y . Based on dimensional analysis, determine the powers x and y by choosing an expression below. 1. μ = A 2 ρ 2. μ = 1 ρ A 2 3. μ = 1 ρ A 4. μ = ρ A correct 5. μ = ρ A 2 6. μ = ρ A 7. μ = A ρ 8. μ = A ρ 2 9. μ = A 2 ρ 2 10. μ = ρ A 2 Explanation: Kilogram (kg): a unit of mass ( M ). Meter (m): a unit of length ( L ). ouseph (jao888) – HW01 – tsoi – (92940) 2 [ x ] means ”the units of x ”. The units of both sides of any equation must be the same for the equation to make sense. The units of the left hand side (LHS) are given as [ μ ] = M L = ML- 1 , and the right hand side has [ ρ x A y ] = parenleftbigg M L 3 parenrightbigg x × ( L 2 ) y = M x L- 3 x L 2 y = M x L 2 y- 3 x , thus M +1 L- 1 = M x L 2 y- 3 x ....
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This note was uploaded on 07/09/2011 for the course PHY 302 taught by Professor Staff during the Summer '08 term at University of Texas at Austin.

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Solution_1 - ouseph(jao888 – HW01 – tsoi –(92940 1 This print-out should have 14 questions Multiple-choice questions may continue on the next

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