This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here are the solutions to the questions from the image: a) Convert 2.5 gmm^-2 to kgm^-2. Step 1: Convert grams (g) to kilograms (kg). We know that 1 g = 10^-3 kg. Step 2: Convert square millimeters (mm^2) to square meters (m^2). We know that 1 mm = 10^-3 m. Therefore, 1 mm^-2 = (10^-3 m)^-2 = 10^6 m^-2. Step 3: Substitute the conversions into the given value. 2.5 gmm^-2 = 2.5 × (10^-3 kg) × (10^6 m^-2) 2.5 gmm^-2 = 2.5 × 10^(-3+6) kgm^-2 2.5 gmm^-2 = 2.5 × 10^3 kgm^-2 The converted value is 2.5 × 10^3 kgm^-2. b) Determine if the formula T = 2 sqrt((m)/(F/x)) is dimensionally correct. Where T is time period, m is mass, F is force and x is distance. Step 1: Determine the dimension of the Left Hand Side (LHS). The LHS is T, which represents time period. Dimension of LHS = [T] Step 2: Determine the dimensions of the terms in the Right Hand Side (RHS). 2 is a dimensionless constant. Dimension of mass (m) = [M] Dimension of force (F) = [M][L][T^-2] Dimension of distance (x) = [L] Step 3: Calculate the dimension of the term (F)/(x). Dimension of (F)/(x) = [M][L][T^-2][L] = [M][T^-2] Step 4: Calculate the dimension of the term (m)/(F/x). Dimension of (m)/(F/x) = ([M])/([M][T^-2)] = (1)/([T^-2)] = [T^2] Step 5: Calculate the dimension of the square root term. Dimension of sqrt((m)/(F/x)) = sqrt([T^2]) = [T] Step 6: Compare the dimensions of LHS and RHS. Dimension of LHS = [T] Dimension of RHS = Dimension of 2 × Dimension of sqrt((m)/(F/x)) = 1 × [T] = [T] Since the dimension of LHS equals the dimension of RHS, the formula is dimensionally correct. The formula is dimensionally correct. c) State the conditions for two vectors to be equal. Give any four examples of the term "magnitude" as applied to vector and scalar quantities. Conditions for two vectors to be equal: 1. They must have the same magnitude. 2. They must have the same direction. 3. They must represent the same physical quantity. Examples of quantities that have magnitude: • Mass (Scalar): e.g., 5 kg • Velocity (Vector): e.g., 20 ms^-1 North • Temperature (Scalar): e.g., 30^ C • Force (