Question
A hollow sphere of radius R lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. Find the distance travelled by the sphere during the time it makes one full rotation.
✓
Answer
Taking moment about the centre of hollow sphere we will get$\text{F}\times\text{R}=\frac{2}{3}\text{MR}^2\alpha$
$\Rightarrow\alpha=\frac{3\text{F}}{2\text{MR}}$
Again, $2\pi=\Big(\frac{1}{2}\Big)\alpha\text{t}^2$ $\Big(\text{From}\ \theta=\omega_0\text{t}+\Big(\frac{1}{2}\Big)\alpha\text{t}^2\Big)$
$\Rightarrow\text{t}^2=\frac{8\pi\text{MR}}{\text{3F}}$
$\Rightarrow\text{a}_{\text{c}}=\frac{\text{F}}{\text{m}}$
$\Rightarrow\text{X}=\Big(\frac{1}{2}\Big)\text{a}_{\text{c}}\text{t}^2=\Big(\frac{1}{2}\Big)=\frac{4\pi\text{R}}{3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R. Draw the magnetic field lines due to a circular wire carrying current I.
What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?
- In the following arrangement of capacitors, the energy stored in the $6 \mu F$ capacitor is $E$. Find the value of the following:
- Energy stored in $12 \mu F$ capacitor.
- Energy stored in $3 \mu F$ capacitor.
- Total energy drawn from the battery.
Describe principle and construction of AC generator with figure and discuss its working.
Three point charges $+Q, -2Q$ and $-3Q$ are placed at the vertices of an equilateral triangle $\text{ABC}$ of side l.
If these charges are displaced to the mid points $A_1, B_1$ and $C_1$ respectively, calculate the amount of work done in shifting the charges to the new locations.
→If these charges are displaced to the mid points $A_1, B_1$ and $C_1$ respectively, calculate the amount of work done in shifting the charges to the new locations.
The geostationary orbit of the earth is at a distance of about $36000\ km$ from the earth's surface. Find the weight of a $120\ kg $ equipment placed in a geostationary satellite. The radius of the earth is $6400\ km.$
→The potential difference between the terminals of a battery of emf 6.0V and internal resistance $1\Omega$ drops to 5.8V when connected across an external resistor. Find the resistance of the external resistor.
→A parallel plate capacitor is charged to a potential difference V from a direct current source, while there is air between the plates. Without separating the capacitor from the battery, a dielectric medium of dielectric constant K has been filled in place of air. Explain with reasons which of the following changes will occur? Also give explanation of the answers.(i) Potential difference (ii) Electric field between the plates (iii) Capacitance (iv) charge (v) energy.
A rectangular wire frame, shown below, is placed in a uniform magnetic field directed upward and normal to the plane of the paper. The part AB is connected to a spring. The spring is stretched and released when the wire AB has come to the position A′ B′ (t = 0) How would the induced emf vary with time? Neglect damping.
Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in vacuum is I/c.