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Seconds Pendulum PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS Measurement of Time and Mass Measurement of Time Measuring time is necessary for any experiment or any activity which one performs. The following instruments help to keep record of time: Stop Watch A stop watch consists of a circular dial graduated in 60 equal spaced divisions. Each division is equal to 1 second. In some watches, each division is divided in two parts enabling us to measure time correct up to 0.5 seconds. A seconds hand is pivoted at the centre of the dial. A small dial is also provided inside the big dial. This dial enables us to record time in minutes. This dial is divided into 60 divisions. When the seconds hand completes one rotation, the minute hand moves by one division. A knob is provided at the top of the frame of the watch for winding purposes. The knob is pressed in succession to bring both the hands to zero, and the stop watch can then be used. The knob is pressed at the start of the event and pressed again to stop time at the end of the event. The reading of time is calculated by adding the time of the minute hand and the time of the second’s hand. Stop Clock It is a table clock and is bigger than a stop watch. It has a circular dial graduated in 60 equally spaced divisions. Each division is equal to 1 second. A second’s hand is pivoted at the centre of the dial. This gives the reading in seconds. www.topperlearning.com 2 PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS To read time in minutes, the minute hand is provided along with the second’s hand, or a separate dial is provided similar to a stop watch. When the seconds hand completes one rotation, the minute hand moves by one division. The minute hand is set to zero by a knob provided at the back of the clock. The clock is also provided with an index hand. It can be set from the outside over the seconds hand at the start of the event to indicate the starting time. It is usually painted red. A horizontal rod is provided at the back of the frame to start or stop the clock. When the rod is pushed to the right, it starts the clock. When it is pushed to the left, it stops the clock. Simple Pendulum A simple pendulum is a heavy point mass called the bob suspended from a rigid support by a massless and inextensible string. NOTE: This is only an ideal definition as a point mass which is heavy and a massless string are practically impossible to produce. www.topperlearning.com 3 PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS When the bob at the rest position is moved to one side and released, the pendulum is set in motion. The rest position is called the mean position of the pendulum. Terms related to Simple Pendulum Oscillation: One complete to-and-fro motion of the bob of the pendulum is called one oscillation. Period of oscillation or time period: It is the time taken to complete one oscillation. It is denoted by T. Its unit is second (s). Frequency of oscillation: It is the number of oscillations made in one second. It is denoted by f or n. Its unit is per second (s−1) or hertz (Hz). Amplitude: The maximum displacement of the bob from its mean position on either side is called the amplitude of oscillation. It is denoted by a or A. Its unit is metre (m). Effective length of the pendulum: It is the distance of the mean point of oscillation to the point of suspension. It is denoted as l. Relation between Time Period and Frequency In one time period T, the number of oscillations of the pendulum is one. In one second, the number of oscillations will be 1/T. 1 Thus, the frequency is f . T Measurement of time period of a simple pendulum To measure the time period, the bob of the pendulum is displaced slightly and released. The time period for a certain number of oscillations is noted. This is repeated for different lengths of the pendulum. It is then noted that the time period is directly proportional to the square root of the length. Tl Tl2 l constant T2 Graph of Variation of Time Period T with Length l The graph of T v/s l of a pendulum is a curve as shown below. www.topperlearning.com 4 PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS Thus, a graph of T v/s l is plotted which is a straight line as shown below. Graph of T2 v/s l The graph of T2 v/s l is a straight line indicating that T2 is directly proportional to l for a pendulum. The slope from the graph is given as PR TT22 Slope 12 QR l l 12 The slope is constant at a place and is given as 42 Slope g www.topperlearning.com 5 PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS here, g is the acceleration due to gravity. Factors Affecting Time Period The time period of oscillation of a pendulum is directly proportional to the square root of its effective length. Tl Due to seasonal changes, the temperature varies, and hence, the time period also varies. During winters, the length of the pendulum (which is generally made of brass or steel) shortens due to contraction. Thus, the time period also shortens. Similarly, during summers, the length and hence the time period increases. The time period of oscillation of a pendulum is inversely proportional to the square root of acceleration due to gravity. 1 T g Thus, at higher altitudes or at depths the pendulum slows down due to decrease in the value of g. The time period of oscillation of a pendulum does not depend on the mass or material of the body suspended. The time period of oscillation of a pendulum does not depend on the extent of swing, i.e. amplitude on either side. Thus, we get the expression of the time period of the pendulum as l T2 g here, T is the time period, l is the length and g is the acceleration due to gravity. Seconds pendulum The pendulum in clocks at our homes is a seconds pendulum. This pendulum has a time period of 2 s. That is, it takes 1 s to move from one extreme to the other. Thus, a seconds pendulum is a pendulum with a time period of oscillation equal to 2 s. Measurement of Mass: A Beam Balance for Comparison of Masses The amount of matter contained in a body is its mass. It is measured by a beam balance by comparing it with a known standard mass. A beam balance works on the principle of moments. According to this principle, “In equilibrium, the moment due to the weight of an object on one side of the beam is equal to the moment due to the standard weights on the other side of the beam”. One moment is clockwise and the other is anticlockwise. www.topperlearning.com 6 PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS A beam balance is shown below. Precautions in Using a Beam Balance The lever should be turned gently in order to prevent the knife edges from chipping. The beam should be lowered before adding or removing weights from the pan. Wet and hot objects should not be placed on the pan. The weights should be placed in the weight box after weighing. The weights should be carried with forceps. When near the actual weight, the weights should always be tried in ascending order. Conditions for a True Balance To be true, a balance must satisfy the following two conditions: o Both the arms must be of equal lengths. o Both the arms must be of equal weights. www.topperlearning.com 7 .
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