# If the length of a simple pendulum is reduced to half and mass is doubled then the time period of simple is

1. Remains unchanged
2. Halved
3. Doubled
4. Decreased by a factor of $\sqrt{2}$

## If the length of a simple pendulum is reduced to half and mass is doubled then the period of simple is

If the length of a simple pendulum is reduced to half and mass is doubled then the period of simple is decreased by a factor of $\sqrt{2}$

$\mathbf{T&space;=&space;2\pi&space;\sqrt{\frac{L}{g}}}$

The time period of a simple pendulum is independent of mass.

$\mathbf{Put&space;\&space;L&space;=&space;\frac{L}{2}&space;}$

$\mathbf{T^{'}&space;=&space;2\pi&space;\sqrt{\frac{L/2}{g}}}$

$\mathbf{T^{'}&space;=&space;2\pi&space;\sqrt{\frac{L}{2g}}}$

$\mathbf{T^{'}&space;=&space;\frac{1}{\sqrt{2}}&space;\left&space;(&space;2\pi&space;\sqrt{\frac{L}{g}}&space;\&space;\right&space;)}$

$\mathbf{T^{'}&space;=&space;\frac{1}{\sqrt{2}}&space;T}$

Hence the period of simple is decreased by a factor of $\sqrt{2}$.

 MSC Physics MCQs 1. Atomic Physics 2. Nuclear Physics 3. Classical Mechanics 4. Quantum Mechanics 5. Electronics Physics 6. Solid State Physics 7. Physical Wave Optics 8. Waves and Oscillations 9. Electromagnetic Theory 10. Special Theory of Relativity 11. Heat and Thermodynamics 12. Mathematical Method for Physics