For a given velocity, a projectile has the same range R for two a… - Vidyadip

MCQ

For a given velocity, a projectile has the same range $R$ for two angles of projection if $t$ and $t$ are the times of flight in the two cases then[KCET 2003

A
$t_1 t_2 \propto R^2$
✓
$t_1 t_2 \propto R$
C
$t_1 t_2 \propto \frac{1}{R}$
D
$t_1 t_2 \propto \frac{1}{R^2}$

✓

Answer

Correct option: B.

$t_1 t_2 \propto R$

(b) For same range angle of projection should be $\theta$ and 90- $\theta$So, time of flights $t_1=\frac{2 u \sin \theta}{g}$ and$t_2=\frac{2 u \sin (90-\theta)}{g}=\frac{2 u \cos \theta}{g}$
$\text { By multiplying }=t_1 t_2=\frac{4 u^2\sin \theta \cos \theta}{g^2} t_1 t_2=\frac{2}{g} \frac{\left(u^2 \sin 2\theta\right)}{g}=\frac{2 R}{g}$
$\Rightarrow t_1 t_2 \propto R$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Motion in Two Dimension→Motion in Two Dimension — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Two tuning forks when sounded together produced $4$ beats/sec. The frequency of one fork is $256.$ The number of beats heard increases when the fork of frequency $256$ is loaded with wax. The frequency of the other fork is

During the adiabatic expansion of $2$ moles of a gas, the internal energy was found to have decreased by $100 \mathrm{~J}$. The work done by the gas in this process is

In a series $L C R$ circuit, operated with an ac of angular frequency $\omega$, the total impedance is

If velocity of a body is twice of previous velocity, then kinetic energy will become

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g / 4$, then the new time period of the pendulum is

Photo cell is a device to

A monochromatic beam of light falls on YDSE apparatus at some angle (say $\theta$ ) as shown in figure. A thin sheet of glass is inserted in front of the lower slit $S$. The central bright fringe (path difference = o) will be obtained

Three weights $W, 2 W$ and $3 W$ are connected to identical springs suspended from a rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that

The velocity of a body moving with a uniform acceleration of $2 m . / sec ^2$ is $10 m / sec$. Its velocity after an interval of $4 sec$ is

An alternating current of frequency ${ }^{\prime} f^{\prime}$ is flowing in a circuit containing a resistance $R$ and a choke $L$ in series. The impedance of this circuit is