Download App

STD 11 - 3.2. motion in plane — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 3.2. motion in plane4 Marks
MCQ
For a given velocity, a projectile has the same range $R$ for two angles of projection if $t_1$ and $t_2$ are the times of flight in the two cases then
  • 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
(b) For same range angle of projection should be $\theta$ and $90-\theta$

So, time of flights ${t_1} = \frac{{2u\sin \theta }}{g}$ and

${t_2} = \frac{{2u\sin (90 - \theta )}}{g} = \frac{{2u\cos \theta }}{g}$

By multiplying$ = {t_1}{t_2} = \frac{{4{u^2}\sin \theta \cos \theta }}{{{g^2}}}$

${t_1}{t_2} = \frac{2}{g}\frac{{({u^2}\sin 2\theta )}}{g} = \frac{{2R}}{g}$

$⇒$ ${t_1}{t_2} \propto R$

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

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

When a mass $m$ is attached to a spring it oscillates with period $4 \,s$. When an additional mass of $2 \,kg$ is attached to a spring, time period increases by $1 \,s$. The value of $m$ is ........... $kg$
→
In a series $R-L-C$ $AC$ circuit, for a particular value of $R, L$ and $C$ power supplied by the source is $P$ at resonance. If the value of inductance is halved, then the power from the  source again at resonance is $P'.$ Then :
→
A ball is rolled off the edge of a horizontal table at a speed of $4\, m/second$. It hits the ground after $0.4\, second$. Which statement given below is true
→
When plate voltage in diode valve is increased from $100\, volt$ to $150 \,volt$ then plate current increases from $7.5\, mA$ to $12\, mA$. The dynamic plastic resistance will be....$k\,\Omega$
→
An achromatic combination of lenses is formed by joining
→
Two masses ${m_1}$ and ${m_2}$ are attached to a string which passes over a frictionless smooth pulley. When ${m_1} = 10kg,$ ${m_2} = 6kg,\,$the acceleration of masses is  .......... $m/s^{2}$
→
If ${N_P}$and ${N_e}$be the numbers of holes and conduction electrons in an extrinsic semiconductor, then
→
A tennis ball dropped from a height of $2 \,m$ rebounds only $1.5 \,m$ after hitting the ground. What fraction of its energy is lost in the impact
→
A surveyor's $30$-$m$ steel tape is correct at some temperutre. On a hot day the tape has expanded to $30.01$ $m$. On that day, the tape indicates a distance of $15.52$ $m$ between two points. The true distance between these points is :-
→
A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be
→