The period of a simple pendulum, whose bob is a hollow metallic sphere, is T . The period is T1 when the bob is filled with sand, T2 when it is filled with mercury and T3 when it is half filled with mercury. Which of the following is true? Hollow Sand Mercury

Question

The period of a simple pendulum, whose bob is a hollow metallic sphere, is T . The period is T1 when the bob is filled with sand, T2 when it is filled with mercury and T3 when it is half filled with mercury. Which of the following is true? Hollow Sand Mercury (A) T = T1 = T2 > T3 (B) T1 = T1 = T3 > T (C) T > T3 > T1 = T2 (D) T = T1 = T2 < T3

Tardigrade Admin · Accepted Answer

Time period of pendulum doesn't depends upon mass but it depends upon length (distance between point of suspension and centre of mass). In first three cases length are same so T=T1=T2 but in last case centre of mass lowers which in turn increases the length. So in this case time period will be more than the other cases.

Q. The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T .$ The period is $T_{1}$ when the bob is filled with sand, $T_{2}$ when it is filled with mercury and $T_{3}$ when it is half filled with mercury. Which of the following is true? Hollow Sand Mercury

$T = T_{1} = T_{2} > T_{3}$

$T_{1} = T_{1} = T_{3} > T$

$T > T_{3} > T_{1} = T_{2}$

$T = T_{1} = T_{2} < T_{3}$

Q. The period of a simple pendulum, whose bob is a hollow metallic sphere, is T. The period is T1​ when the bob is filled with sand, T2​ when it is filled with mercury and T3​ when it is half filled with mercury. Which of the following is true? Hollow Sand Mercury

T=T1​=T2​>T3​

T1​=T1​=T3​>T

T>T3​>T1​=T2​

T=T1​=T2​<T3​

Q. The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T .$ The period is $T_{1}$ when the bob is filled with sand, $T_{2}$ when it is filled with mercury and $T_{3}$ when it is half filled with mercury. Which of the following is true? Hollow Sand Mercury

$T = T_{1} = T_{2} > T_{3}$

$T_{1} = T_{1} = T_{3} > T$

$T > T_{3} > T_{1} = T_{2}$

$T = T_{1} = T_{2} < T_{3}$