A bob hangs from a rigid support by an inextensible string of length (from the lowest position) keeping the string straight, and then released. The speed of the bob at the lowest position is
A.
B.
C.
D.
Answer
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Hint: We need to use the principle of conservation of energy between the highest point and the lowest point. For calculation of potential energy, find the vertical distance of the bob at the highest position from the lowest position.
Formula used:
In this solution we will be using the following formulae;
where is the potential energy of a body from a reference point, is the mass of that body, is the acceleration due to gravity and is the vertical height of the body from the reference point.
where is the kinetic energy of the body, and is the velocity of the body.
Complete answer:
First, we see from diagram, that the height of the bob above the lowest point can be given by
Now, using the lowest point as the reference point, the potential energy of the bob can be found using the formula
where is the mass of that body, is the acceleration due to gravity and is the vertical height of the body from the reference point.
Hence,
Now, according to the principle of conservation of energy, all the potential at the highest point will be converted to kinetic energy at the lowest point. The kinetic energy is
where is the velocity of the body.
Hence,
Hence, by making subject of the formula, we have
Hence, the correct option is A.
Note:
For clarity, note that the point of reference is not essential to the calculation of the velocity, any point can be used as a reference point. The potential energy is always based on some point of reference.
Formula used:
In this solution we will be using the following formulae;
Complete answer:
First, we see from diagram, that the height of the bob above the lowest point can be given by
Now, using the lowest point as the reference point, the potential energy of the bob can be found using the formula
Hence,
Now, according to the principle of conservation of energy, all the potential at the highest point will be converted to kinetic energy at the lowest point. The kinetic energy is
Hence,
Hence, by making
Hence, the correct option is A.
Note:
For clarity, note that the point of reference is not essential to the calculation of the velocity, any point can be used as a reference point. The potential energy is always based on some point of reference.
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