A stone of mass $2 \mathrm{~kg}$ is whirled in a horizontal circle attached at the end of a $1.5 \mathrm{~m}$ long string. If the string makes an angle of $30^{\circ}$ with the vertical, compute its period.
Q 52.1
Download our app for free and get started
Data : $L=1.5 \mathrm{~m}, \theta=30^{\circ}, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$
The period of the conical pendulum,
$
\begin{aligned}
T & =2 \pi \sqrt{\frac{L \cos \theta}{g}}=2 \times 3.142 \times \sqrt{\frac{1.5 \cos 30^{\circ}}{10}} \\
& =6.284 \times \sqrt{\frac{1.5 \times 0.866}{10}}=6.284 \sqrt{\frac{1.299}{10}} \\
& =2.265 \mathrm{~s} \quad
\end{aligned}
$
The period of the conical pendulum,
$
\begin{aligned}
T & =2 \pi \sqrt{\frac{L \cos \theta}{g}}=2 \times 3.142 \times \sqrt{\frac{1.5 \cos 30^{\circ}}{10}} \\
& =6.284 \times \sqrt{\frac{1.5 \times 0.866}{10}}=6.284 \sqrt{\frac{1.299}{10}} \\
& =2.265 \mathrm{~s} \quad
\end{aligned}
$
Download our appand get started for free
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.*
Similar Questions
- 1A flywheel slows down uniformly from $1200 \mathrm{rpm}$ to $600 \mathrm{rpm}$ in $5 \mathrm{~s}$. Find the number of revolutions made by the wheel in $5 \mathrm{~s}$.View Solution
- 2View SolutionState an expression for the moment of inertia of a thin ring about its transverse symmetry axis.
- 3Calculate the moment of inertia of a ring of mass $500 \mathrm{~g}$ and radius $0.5 \mathrm{~m}$ about an axis of rotation passing throughView Solution
(i) its diameter
(ii) a tangent perpendicular to its plane. - 4View SolutionOn what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
- 5State the expression for the Ml of a thin spherical shell (i.e., a thin-walled hollow sphere) about its diameter. Hence obtain the expression for its $\mathrm{Ml}$ about a tangent.View Solution
- 6View SolutionWhat is the recommendations on loading a vehicle for not toppling easily?
- 7View SolutionWhy do grinding wheels have large mass and moderate diameter?
- 8View SolutionWhat do you do if your vehicle is trapped on a slippery or sandy road? What is the physics involved?
- 9View SolutionState the MI of a thin rectangular plate-of mass M, length l and breadth b- about an axis passing through its centre and parallel to its length. Hence find its MI about a parallel axis along one edge.
- 10Assuming the expression for the moment of inertia of a thin uniform disc about its diameter, show that the moment of inertia of the disc about a tangent in its plane is $\mathrm{MR}^2$. Write the expression for the corresponding radius of gyration.View Solution