D. C. Pandey Solutions for Chapter: Engineering Entrance Solved Papers 2018 JEE Main & Advanced/BITSAT/KCET/Andhra Pradesh & Telangana (EAMCET)/VIT/MHT CET, Exercise 1: AP EAMCET

A car moves in positive $y$-direction with velocity $v$ proportional to distance travelled $y$ as $v\left(y\right)\propto y^{\beta }$, where $\beta$ is a positive constant. The car covers a distance $L$ with average velocity proportional to $L$ as . The constant $\beta$ is given as

Consider a particle moving along the positive direction of $X$-axis. The velocity of the particle is given by $V=\alpha \sqrt{x}$ ($\alpha$ is a positive constant). At time $t=0$, if the particle is located at $x=0$, the time dependence of the velocity and the acceleration of the particle are respectively

Find the magnitude of velocity and acceleration and velocity of a particle moving in a plane, whose position vector $r=3t^2 \hat{\mathrm{i}}+2t\hat{\mathrm{j}}+\hat{\mathrm{k}}$ at $t=2 \mathrm{s}$ are respectively

Two objects are located at height $10 \mathrm{m}$ above the ground. At some point of time, the objects are thrown with initial velocity $2\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $45°$ and $135°$ with the positive $X$-axis, respectively. Assuming $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, the velocity vectors will be perpendicular to each other at time is equal to

String $AB$ of unstretched length, $L$ is stretched by applying a force $F$ at the mid point $C$ such that the segments $AC$ and $BC$ make an angle $\theta$ with $AB$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$ The force $F$ is given by

A block of mass $5 \mathrm{kg}$ is kept against an accelerating wedge with a wedge angle of $45°$ to the horizontal. The coefficient of friction between the block and the wedge is $\mu =0.4$. What is the minimum absolute value of the acceleration of the wedge to keep the block steady? [Assume, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

An object moves along the circle with normal acceleration proportional to $t^{\alpha }$, where $t$ is the time and $\alpha$ is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to,

A ball of mass $1 \mathrm{kg}$ moving along $x$-direction collides elastically with a stationary ball of mass $m$. The first ball (mass $=1 \mathrm{kg}$) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle $30°$ with the $X$-axis, then the value of $m$ must be,