Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is $100 g$. The time period of the motion of the particle will be (approximately) (take $g =10\,ms ^{-2}$, radius of earth $=6400\,km$ )
A bead of mass $m$ is attached to the mid-point of a tant, weightless string of length $l$ and placed on a frictionless horizontal table.Under a small transverse displacement $x$, as shown in above figure. If the tension in the string is $T$, then the frequency of oscillation is
Two particles $P$ and $Q$ start from origin and execute Simple Harmonic Motion along $X-$axis with same amplitude but with periods $3$ seconds and $6$ seconds respectively. The ratio of the velocities of $ P$ and $Q$ when they meet is
Two particles P and Q describe S.H.M. of same amplitude $a$, same frequency $f$ along the same straight line. The maximum distance between the two particles is a $\sqrt{2}$.The initial phase difference between the particle is -
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$ and $16 \mathrm{~ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{\mathrm{x}} \mathrm{m}$ where $\mathrm{x}$ is. . . . . . .
A mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs is