Question:
A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane. If the torque experienced by the hollow sphere and solid sphere are $\tau_H$ and $\tau_S$ respectively, then
A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane. If the torque experienced by the hollow sphere and solid sphere are $\tau_H$ and $\tau_S$ respectively, then
Updated On: Apr 26, 2024
- $\tau_H < \tau_S$
- $\tau_H > \tau_S$
- $\tau_H = \tau_S$
- $\tau_H = 0 $
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
As we know, moment of inertia of hollow
sphere $I_{H}=\frac{2}{3} M R^{2}$ and moment of inertia of solid
sphere $I_{S}=\frac{2}{5} M R^{2}$
$\therefore I_{H}>I_{S}$
Since, torque $=I \alpha$
$\Rightarrow$ Torque $\left(\tau_{H}\right)>$ Torque $\left(\tau_{S}\right)$
sphere $I_{H}=\frac{2}{3} M R^{2}$ and moment of inertia of solid
sphere $I_{S}=\frac{2}{5} M R^{2}$
$\therefore I_{H}>I_{S}$
Since, torque $=I \alpha$
$\Rightarrow$ Torque $\left(\tau_{H}\right)>$ Torque $\left(\tau_{S}\right)$
Was this answer helpful?
0
0
Top Questions on torque
- A uniform magnetic field of \( 2 \times 10^{-3} \, \text{T} \) acts along positive Y-direction. A rectangular loop of sides 20 cm and 10 cm with current of 5 A is in the Y-Z plane. The current is in anticlockwise sense with reference to the negative X-axis. Magnitude and direction of the torque is:
- A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field 𝐵⃗ pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height 𝐿, is placed in the x-y plane with its vertex P at x = 0 in the orientation shown in the figure. At 𝑡 = 0, the loop starts entering the region of the magnetic field with a uniform velocity 𝑣 along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graph best depicts the variation of the induced emf (E) in the loop as a function of the distance (𝑥) starting from 𝑥 = 0? - The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50 \%$ The percentage change in voltage sensitivity of the galvanometer will be:
- The torque acting on a magnetic dipole placed in uniform magnetic field is zero, when the angle between the dipole axis and the magnetic field is _____.
- A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at the 40.0 cm mark. The mass of the metre scale is found to be \(x\times 10^{-2}\) kg. The value of x is _________.
View More Questions
Questions Asked in VITEEE exam
- Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
- VITEEE - 2023
- work, energy and power
- Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes. - The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
- Which element has more electron gain enthalpy among chalcogen group?
- VITEEE - 2022
- sulphur
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Random Variables
View More Questions
Concepts Used:
Torque
Torque is a moment of force. Torque is measured as a force that causeque is also defined as the turning effect of force on the axis of rotation. Torque is chs an object to rotate about an axis and is responsible for the angular acceleration. Characterized with “T”.
How is Torque Calculated?
Torque is calculated as the magnitude of the torque vector T for a torque produced by a given force F
T = F. Sin (θ)
Where,
r - length of the moment arm,
θ - the angle between the force vector and the moment arm.
Read More: Torque
Types of Torque
Torque is of two types:
- Static torque
- Dynamic torque