Question:
If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take
If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take
Updated On: Jul 6, 2024
- 96 h
- 48 h
- 6 h
- 1.5 h
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
We know that angular momentum of spin $=I \omega$
By the conservation of angular momentum
$\frac{2}{5} M R^{2} \cdot \frac{2 \pi}{T}=\frac{2}{5} M\left(\frac{R}{4}\right)^{2} \cdot \frac{2 \pi}{T'}$
$T'=\frac{T}{16}=\frac{24}{16}=1.5\, h$
By the conservation of angular momentum
$\frac{2}{5} M R^{2} \cdot \frac{2 \pi}{T}=\frac{2}{5} M\left(\frac{R}{4}\right)^{2} \cdot \frac{2 \pi}{T'}$
$T'=\frac{T}{16}=\frac{24}{16}=1.5\, h$
Was this answer helpful?
1
0
Top KCET Physics Questions
- The magnetic Lorentz force experienced by a charge q, entering a magnetic field B with a velocity v is
- ABCD is a square loop made of an uniform conducting wire. The current enters the loop at A and leaves at D. The magnetic field is
- A milliammeter of range 10 mA has a coil of resistance $1\Omega$. To use it as a voltmeter of range 10 V, the resistance that must be connected in series with it is
- The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is
- The relative permeability is represented by $\mu_r$ and the susceptibility by $\varkappa$ for a magnetic substance. Then for a paramagnetic substance
View More Questions
Top KCET System of Particles & Rotational Motion Questions
- A door of $1.6\, m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4\, m$ distant from the hinges for opening or closing the door is
- A rotating wheel changes angular speed from $1800\,rpm$ to $3000\, rpm$ in $20\,s$. What is the angular acceleration assuming to be uniform ?
- A solid sphere of mass $m$ rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is $v$. The kinetic energy of the sphere at the bottom is
- Moment of Inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is $I$. If the same rod is bent into a ring and its moment of inertia about its diameter is $I'$, then the ratio ${\frac {I}{I'}}$ is
- A force $F=5 \hat{i}+2\hat{j}-5 \hat{k}$ acts on a particle whose position vector is $r=\hat{i}-2 \hat{j}+\hat{k}$ What is the torque about the origin?
View More Questions
Top KCET Questions
- Which of the following is not true for oxidation?
- If $a, b$ and $c \in N$ which one of the following is not true ?
- When $50\, cm ^{3}$ of $0.2\, N$ $H_{2} SO _{4}$ is mixed with $50 cm ^{3}$ of $1 N\, KOH$, the heat liberated is :
- If $a | (b + c)$ and $a| (b-c)$ where $a,b,c \in \, N $ then
- Which of the following is NOT a pair of functional isomers?
View More Questions