Question
Explain the motion of a boat floating in water. Find the expression of its period.

Answer

SELF

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.
A spring balance reads 10kg when a bucket of water is suspended from it. What is the reading on the spring balance when:
  1. An ice cube of mass 1.5kg is put into the bucket?
  2. An iron piece of mass 7.8kg suspended by another string is immersed with half its volume inside the water in the bucket (Relative density of iron = 7.8)?
Two charges $2.0 \times 10^{-6}C$ and $1.0 \times 10^{-6}C$ are placed at a separation of 10cm. Where should a third charge be placed such that it experiences no net force due to these charges?
Figure (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. (b) is stretched by the same force F.
If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case?
One end of a long string of linear mass density $8.0 \times 10^{–3}kg m^{–1}$ is connected to an electrically driven tuning fork of frequency $256Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t = 0$, the left end (fork end) of the string $x = 0$ has zero transverse displacement $(y = 0)$ and is moving along positive y-direction. The amplitude of the wave is $5.0cm$. Write down the transverse displacement y as function of x and t that describes the wave on the string.
A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the centre of the solenoid is found to be zero.
  1. Find the current in the solenoid.
  2. If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre ?
Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii $R_1$ and $R_2$.
A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute S.H.M. with a time period.$\text{T}=2\pi\sqrt{\frac{\text{m}}{\text{A}\rho\text{g}}}$
where m is mass of the body and ρ is density of the liquid.
A rocket is fired vertically with a speed of $5 \mathrm{~km} \mathrm{~s}^{-1}$ from the earth's surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth $=6.0 \times 10^{24} \mathrm{~kg}$; mean radius of the earth $=6.4 \times 10^6 \mathrm{~m} ; \mathrm{G}=6.67$ $\times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$.
One mole of an ideal gas undergoes a process $\text{p}=\frac{\text{p}_0}{1+\Big(\frac{\text{V}}{\text{V}_0}\Big)^2}$ where $P_0$ and $V_0$ are constants. Find the temperature of the gas when $V = V_0$.