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4 marksPhysical Quantities

CAPE Physics Unit 1 · May/June 2023 · Paper 2 · Question 1(e)(iii)

The experiment was repeated for different values of M at fixed m = 0.013 kg and r = 0.80 m (Table 2).

Write the equation T = 2π √(mr / Mg) in the form y = mx + c to show that the gradient is 4π^2 mr / g. From your graph in (e)(ii), determine an experimental value for the gradient.

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Other parts of this question

  1. 1(a)Differentiate between 'precision' and 'accuracy'.[2 marks]
  2. 1(b)(i)Comment on the accuracy of the results in Table 1. Justify your response.[2 marks]
  3. 1(b)(ii)Comment on the precision of the results in Table 1. Justify your response.[2 marks]
  4. 1(c)The formula for centripetal force is F = mv^2 / r. Write an expression to determine the fractional error in F, given the fractional error in m, v, and r.[1 mark]
  5. 1(d)(i)State the TWO conditions that must be satisfied if a body is moving with uniform circular motion.[2 marks]
  6. 1(d)(ii)Show that the relationship between the period, T, the radius, r, and the masses, m and M, is given by T = 2π √(mr / Mg).[4 marks]
  7. 1(e)(i)Complete Column 3 (1/M) and Column 4 (T^2) of Table 2.[2 marks]
  8. 1(e)(ii)On the grid provided in Figure 2, plot a graph of T^2 versus 1/M. Draw the line of best fit through the points.[4 marks]
  9. 1(e)(iv)Using the equation for the gradient and the experimental value obtained in (e)(iii), calculate an experimental value for g.[2 marks]
  10. 1(f)State, in words, Newton's law of universal gravitation.[2 marks]
  11. 1(g)With the aid of a sketch, explain why the equation E_p = mgh (where g = 9.81 m s^-2) cannot be used to calculate the potential energy of an orbiting Earth…[3 marks]

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