A block of mass $2\,kg$ moving on a horizontal surface with speed of $4\,ms ^{-1}$ enters a rough surface ranging from $x =0.5\,m$ to $x =1.5\,m$. The retarding force in this range of rough surface is related to distance by $F =- kx$ where $k =12\,Nm ^{-1}$. The speed of the block as it just crosses the rough surface will be ........... $\,ms ^{-1}$
JEE MAIN 2022, Difficult
Download our app for free and get started
$a=\frac{- kx }{2}=\frac{-12 x }{2}=-6 x$
$\frac{ v d v }{ dx }=-6 x$
$\int \limits_{4}^{*} vdv =-\int \limits_{\frac{1}{2}}^{ s / 2} 6 xdx$
$\frac{ v ^{2}-4^{2}}{2}=-\frac{6}{2}\left[\left(\frac{3}{2}\right)^{2}-\left(\frac{1}{2}\right)^{2}\right]$
$v ^{2}-16=-6\left(\frac{9}{4}-\frac{1}{4}\right)$
$v ^{2}=16-6 \times 2=4$
$V =2\,m / s$
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
- 1For the given figure, if block remains in equilibrium position then find frictional force between block and wall ........ $N$View Solution
- 2Someone is using a scissors to cut a wire of circular cross section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2 \alpha$. The friction coefficient between the blades and the wire, is :-View Solution
- 3The normal reaction $'{N}^{\prime}$ for a vehicle of $800\, {kg}$ mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is $...\,\times 10^{3}\, {kg} {m} / {s}^{2}$ [Given $\left.\cos 30^{\circ}=0.87, \mu_{{s}}=0.2\right]$View Solution
- 4The tension $T$ in the string shown in figure is ..................... $N$View Solution
- 5A force of $19.6\, N$ when applied parallel to the surface just moves a body of mass $10 \,kg$ kept on a horizontal surface. If a $5\, kg$ mass is kept on the first mass, the force applied parallel to the surface to just move the combined body is........ $N.$View Solution
- 6A block of $1\, kg$ is stopped against a wall by applying a force $F$ perpendicular to the wall. If $\mu = 0.2$ then minimum value of $F$ will be ....... $N.$View Solution
- 7A bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3,$ how far will the block slide approximately?View Solution
- 8The coefficient of static friction, $\mu _s$ between block $A$ of mass $2\,kg$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks $B$ so that the two blocks do not move? The string and the pulley are assumed to be smooth and masseless ....... $kg$ $(g = 10\,m/s^2)$View Solution
- 9A body of $5\, kg$ weight kept on a rough inclined plane of angle $30^o$ starts sliding with a constant velocity. Then the coefficient of friction isView Solution
- 10A block of mass $5\,kg$ is placed at rest on a table of rough surface. Now, if a force of $30\,N$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50\,m$ in an interval of time $10\,s$. Coefficient of kinetic friction is (given, $g =10\,ms ^{-2}$)View Solution