Two wires of the same material have resistances R1 and R2. The first wire has length L1 and diameter D1. The second wire has length L2 and diameter D2. Express R2/R1 in terms of L1, L2, D1, D2.

Question 15: Resistance of a wire Step 1: Recall the formula for resistance. The resistance (R) of a wire is given by: R = (L)/(A) Where is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area. Step 2: Express the cross-sectional area in terms of diameter. The cross-sectional area of a circular wire is A = r^2, where r is the radius. Since the diameter D = 2r, we have r = D/2. A = ((D)/(2))^2 = ( D^2)/(4) Step 3: Substitute the area into the resistance formula. R = (L)/( D^2)4 = (4 L)/( D^2) Step 4: Set up a ratio for the two wires. Since both wires are made of the same material, their resistivity () is the same. The term (4)/() is constant for both wires. Let R_1, L_1, D_1 be the resistance, length, and diameter of the first wire, and R_2, L_2, D_2 for the second wire. (R_2)/(R_1) = (4 L_2)/( D_2^2)(4 L_1)/( D_1^2) (R_2)/(R_1) = (L_2)/(D_2^2) × (D_1^2)/(L_1) (R_2)/(R_1) = ((L_2)/(L_1)) × ((D_1)/(D_2))^2 Step 5: Substitute the given values. Given: • L_1 = 20.0 m • D_1 = 1.50 mm • R_1 = 21.5 • L_2 = 35.0 m • D_2 = 3.0 mm (R_2)/(21.5 ) = (35.0 m20.0 m) × (1.50 mm3.0 mm)^2 (R_2)/(21.5 ) = (1.75) × (0.5)^2 (R_2)/(21.5 ) = 1.75 × 0.25 (R_2)/(21.5 ) = 0.4375 Step 6: Solve for R_2. R_2 = 0.4375 × 21.5 R_2 = 9.40625 Comparing this value to the options, 9.40625 is closest to 11.0 . The resistance of the second wire is approximately d) 11.0 . --- Question 16: Acceleration of an object with constant velocity Step 1: Understand the definition of acceleration. Acceleration is the rate of change of velocity. a = ( v)/( t) Step 2: Apply the definition to constant velocity. If an object moves with a constant velocity, it means its velocity is not changing. Therefore, the change in velocity ( v) is zero. Step 3: Calculate the acceleration. Since v = 0, the acceleration (a) must be zero. a = (0)/( t) = 0 m/s^2 The acceleration of the object is b) Zero. --- Question 17: Distance directly proportional to time Step 1: Interpret "distance covered by an object is directly proportional to time". This means that if d is distance and t is time, then: d t This can be written as d = k t, where k is a constant of proportionality. Step 2: Relate this to velocity. Velocity (v) is defined as the rate of change of distance with respect to time: v = (dd)/(dt) If d = k t, then differentiating with respect to time gives: v = (d)/(dt)(kt) = k Since k is a constant, the velocity (v) is constant. Step 3: Conclude the type of motion. An object moving with constant velocity is said to travel with constant speed (assuming the direction is also constant, which is implied by "distance covered" in a single direction). The object is said to travel with b) Constant speed.