A cuboidal piece of wood has dimensions a, b | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The time period $T$ of $SHM$ for a floating body undergoing small vertical oscillations is given by $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the

Vedclass · Accepted Answer

$2\pi \sqrt{\frac{da}{g}}$

Vedclass · Answer

(D) The time period $T$ of $SHM$ for a floating body undergoing small vertical oscillations is given by $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the depth of the object submerged in the liquid at equilibrium.According to the law of floatation,the weight of the object equals the weight of the displaced liquid:$V_{total} \cdot \rho_{object} \cdot g = V_{submerged} \cdot \rho_{water} \cdot g$$(abc) \cdot d \cdot g = (b \cdot c \cdot l) \cdot 1 \cdot g$Simplifying the equation:$abc \cdot d = bcl$$l = da$Substituting $l$ into the time period formula:$T = 2\pi \sqrt{\frac{da}{g}}$

$A$ cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side $a$ is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is:

Similar Questions

If the length of a second's pendulum is decreased by $2\%$,how many seconds will it lose per day?

$A$ simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position,the frequency of its oscillations will be

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)

$A$ pendulum clock keeps correct time at $0^{\circ}C$. If its mean coefficient of linear expansion is $\alpha /^{\circ}C$,what is the loss in seconds per day by the clock if the temperature rises by $t^{\circ}C$?

$A$ simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration,the frequency of the simple pendulum will

Vedclass Test Series

Exam Paper Generator

Online Exam Module