A small solid ball is dropped from a height a | vedclass

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

Question

(A) Let the density of the ball be $\rho_b = 500 \ kg/m^3$ and the density of the liquid be $\rho_l = 1000 \ kg/m^3$. Let $V$ be the volume of the bal

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(A) Let the density of the ball be $ho_b = 500 \ kg/m^3$ and the density of the liquid be $ho_l = 1000 \ kg/m^3$. Let $V$ be the volume of the ball.When the ball is inside the liquid,the forces acting on it are the buoyant force $F_B = V ho_l g$ (upwards) and the weight $W = V ho_b g$ (downwards).The net force $F_{net} = F_B - W = V ho_l g - V ho_b g = V g (ho_l - ho_b)$.The acceleration $a$ of the ball inside the liquid is $a = \frac{F_{net}}{m} = \frac{V g (ho_l - ho_b)}{V ho_b} = g \frac{(ho_l - ho_b)}{ho_b}$.Substituting the values: $a = 10 	imes \frac{(1000 - 500)}{500} = 10 	imes \frac{500}{500} = 10 \ m/s^2$ (upwards).Let $v_0$ be the velocity of the ball when it strikes the liquid surface. Using the equation of motion $v = u + at$ for the motion inside the liquid,where the final velocity is $0$ at $t = 2 \ s$:$0 = v_0 - a t \Rightarrow v_0 = a t = 10 	imes 2 = 20 \ m/s$.For the free fall from height $h$,$v_0^2 = 2gh$.$20^2 = 2 	imes 10 	imes h \Rightarrow 400 = 20h \Rightarrow h = 20 \ m$.

Similar Questions

An object of volume $V_0$ and density $d_0$ is placed in a liquid of density $d$. What fraction of its volume remains outside the liquid?

Two cylinders of same cross-section and length $L$ but made of two materials of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length $L/2$ above the surface of the liquid. If $d_1 > d_2$,then:

The fraction of a floating object of volume $V_0$ and density $d_0$ above the surface of a liquid of density $d$ will be

What is buoyant force?

Vedclass Test Series

Exam Paper Generator

Online Exam Module