The acceleration due to gravity on the surface of moon is 1.7 ms-2.What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms-2
Acceleration due to gravity on the surface of moon, g'=1.7 ms-2
Acceleration due to gravity on the surface of earth, g=9.8 ms-2
Time period of a simple pendulum on earth, T=3.5 s
\(T=2π\sqrt\frac{l}{g}\)
Where,
l is the length of the pendulum
\(∴l=\frac{T^2}{(2π)^2}×g\)
\(=\frac{(3.5)^2}{4×(3.14)^2}×9.8 m\)
The length of the pendulum remains constant.
On moon’s surface, time period, \(T'=2π\sqrt\frac{l}{g'}\)
\(=2π\sqrt\frac{\frac{(3.5)^2}{4×(3.14)^2}×9.8}{1.7}=8.4 s\)
Hence, the time period of the simple pendulum on the surface of moon is 8.4 s.
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity):
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
Find the mean deviation about the median for the data
xi | 15 | 21 | 27 | 30 | 35 |
fi | 3 | 5 | 6 | 7 | 8 |