MCQ
A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be
- AA straight line
- BAn arc of a circle
- ✓A parabola
- DAn ellipse
✓
Answer
Correct option: C.
A parabola
c
(c) A particle moves with constant acceleration in a direction different from initial
(c) A particle moves with constant acceleration in a direction different from initial
velocity. Let the velocity be $v,$ acceleration be $a,$ angle between them is $\theta\left[\theta<90^{0}\right]$
Component of Velocity in the Direction of $a$ is $v \cos \theta$ and in a direction perpendicular to $a$ is vsin $\theta$
From equations of Kinematics, In the direction of acceleration, $y=v \cos \theta t+\frac{1}{2} a t^{2}-----(1)$
In the direction perpendicular to acceleration,
$x=v \sin \theta t$
$t=\frac{x}{v \sin \theta}--------(2)$
Substituting 2 in $1,$ we get:
$y=v \cos \theta\left(\frac{x}{v \sin \theta}\right)+\frac{1}{2} a\left(\frac{x^{2}}{\sin ^{2} \theta}\right)$
$y=\frac{x}{\tan \theta}+\frac{1}{2} a \frac{x^{2}}{\sin ^{2} \theta}$
This is in the form of a parabola: $y=A x^{2}+B x+C$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the external force acting on a system have zero resultant, the centre of mass:
- Must not move.
- Must not accelerate.
- May move.
- May accelerate.
A drop of liquid of radius $\mathrm{R}=10^{-2} \mathrm{~m}$ having surface tension $\mathrm{S}=\frac{0.1}{4 \pi} \mathrm{Nm}^{-1}$ divides itself into $\mathrm{K}$ identical drops. In this process the total change in the surface energy $\Delta U=10^{-3} \mathrm{~J}$. If $\mathrm{K}=10^\alpha$ then the value of $\alpha$. . . . is
→Young's modulus of a material has the same unit as:
A body is executing Simple Harmonic Motion. At a displacement $x$ its potential energy is ${E_1}$ and at a displacement y its potential energy is ${E_2}$. The potential energy $E$ at displacement $(x + y)$ is
→A wooden block of mass $5 \mathrm{~kg}$ rests on soft horizontal floor. When an iron cylinder of mass $25$ $\mathrm{kg}$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1 \mathrm{~ms}^{-2}$. The action force of the system on the floor is equal to:
→The amount of work, which can be obtained by supplying $200\, cal$ of heat, is
→Water flows in a horizontal tube as shown in figure. The pressure of water changes by $600\, N/ m^2$ between $A$ and $B$ where the area of crosssection are $30\, cm^2$ and $15\, cm^2$ respectively. Find the rate of flow of water through the tube.
→A river is flowing from $W$ to $E$ with a speed of $5 \,m/min$. A man can swim in still water with a velocity $10\, m/min$. In which direction should the man swim so as to take the shortest possible path to go to the south.
→$1$ joule of energy is to be converted into new system of units in which length is measured in $10$ metre, mass in $10 \,kg$ and time in $1$ minute. The numerical value of $1 \,J$ in the new system is
→If the velocity of a particle is $v =At+ Bt^2$ ,where $A$ and $B$ are constants, then the distance travelled by it between $1\, s$ and $2\, s$ is
→