A Spherical ball of radius $1 mm$ and density $10.5 g / cc$ is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5 g / cc$. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} N$. The value of $x$ is $\text { (Given, } g =9.8 m / s ^2 \text { and } \pi=\frac{22}{7} \text { ) }$
JEE MAIN 2023, Medium
Download our app for free and get started
When the ball attain terminal velocity
$F _r=\left( mg - F _{ B }\right)(\because a =0)$
$= V \sigma_{ b } g - V \rho_{\ell} g$
$= Vg \left(\sigma_{ b }-\rho_{\ell}\right)$
$=\frac{4}{3} \pi\left(10^{-3}\right)^3 \times 9.8(10.5-1.5) \times 10^3$
$=3696 \times 10^{-7}\,N$
So, $x=7$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A wooden block of volume $1000\, cm^3$ is suspended from a spring balance. It weighs $12$ $N$ in air. It is suspended in water such that half of the block is below the surface of water. The reading of the spring balance is ...... $N$View Solution
- 2An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force as shown below.When the spring object system is immersed in a liquid of density $\rho_1$ as shown in the above figure, the spring stretches by an amount $x_1\left(\rho > \rho_1\right)$. When the experiment is repeated in a liquid of density $\left(\rho_2 < \rho_1\right)$, the spring stretches by an amount $x_2$. Neglecting any buoyant force on the spring, the density of the object isView Solution
- 3A cylinder of height $ 20\; m$ is completely filled with water. The velocity of efflux of water (in $ m/s$) through a small hole on the side wall of the cylinder near its bottom is ....... $m/s$View Solution
- 4A train with cross-sectional area $S _{ t }$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S _0\left( S _0=4 S _{ t }\right)$. Assume that almost all the air (density $\rho$ ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $p _0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$, then $p _0- p =\frac{7}{2 N } \rho v_{ t }^2$. The value of $N$ is. . . . .View Solution
- 5$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.View Solution
$Reason :$ According to Bernoulli’s theorem, for the stream line flow of an ideal liquid, the total energy per unit mass remains constant. - 6Two capillaries of same length and radii in the ratio $1 : 2$ are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is $ 1 m$ of water, the pressure difference across first capillary is...... $m$View Solution
- 7View SolutionIncrease in pressure at one point of the enclosed liquid in equilibrium of rest is transmitted equally to all other points of liquid. This is as per ...........
- 8A liquid of density $10^3 \,kg / m ^3$ and coefficient of viscosity $8 \times 10^{-2} \;decapoise$ is flowing in a tube of radius $2 \,cm$ with speed $2 \,m / s$. The Reynold's number is ..........View Solution
- 9Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is $P$ at a point where flow speed is $v$ , the pressure at another point where the flow speed is $2v$ , is (Take density of water as $\rho $ )View Solution
- 10The diagram (figure) shows a venturimeter, through which water is flowing. The speed of water at $X$ is $2\,cm/s.$ The speed of water at $Y$ (taking $g = 1000 \,cm/s^2$ ) is ........ $cm/s$View Solution
