A simple pendulum consists of a point mass suspended by a weightless, rigid wire in a uniform gravitation field. Which of the fo
llowing statements are true when the system undergoes small oscillations? Check all that apply. a. The period is independent of the length of the wire. b. The period is inversely proportional to the length of the wire. c. The period is independent of the suspended mass. d. The period is proportional to the suspended mass. e. The period is proportional to the square root of the length of the wire. f. The period is inversely proportional to the suspended mass.
In case of a simple pendulum having suspended mass 'M', if the length of the wire is 'L', and the acceleration due to gravity that acts on it is 'g', then the time period, 'T' of the pendulum for one complete oscillation is given by:
From the above equation, we can say that:
Time period of the pendulum does not depend on the suspended mass.
Time period is in direct proportion to the square root of the wire length
Time period is depends inversely on the acceleration due to gravity.
To solve this problem we will apply the concepts related to the thermal efficiency given in an engine of the Carnot cycle. Here we know that efficiency is given under the equation
Where,
Temperature of Cold Body
Temperature of Hot Body
= Efficiency
According to the statement our values are:
Replacing we have that
Therefore the temperature of the heat source is 300K
If we draw the path of the van then we get a shape with two exposed points A and D. If we draw a line from point D perpendicular to BA we get point E. This gives us a right angled triangle ADE.