Physics (AS & A Level) · May / June 2020 · Paper 42 · Question 4

A dish is made from a section of a hollow glass sphere. The dish, fixed to a horizontal table, contains a small solid ball of mass 45 g, as shown in Fig. 4.1. C ball mass 45 g surface of dish x Fig. 4.1 The horizontal displacement of the ball from the centre C of the dish is x. Initially, the ball is held at rest with distance x = 3.0 cm. The ball is then released. The variation with time t of the horizontal displacement x of the ball from point C is shown in Fig. 4.2. –4 –2 –3 0 –1 2 1 x / cm t / s 3 4 1 0 2 3 4 7 6 5 Fig. 4.2 The motion of the ball in the dish is simple harmonic with its acceleration a given by the expression a = –(g R) x where g is the acceleration of free fall and R is a constant that depends on the dimensions of the dish and the ball.

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