MCQ

      Column $-I$

    Angle of projection

    Column $-II$
  $A.$ $\theta \, = \,{45^o}$   $1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$
  $B.$ $\theta \, = \,{60^o}$   $2.$ $\frac{{g{T^2}}}{R} = 8$
  $C.$ $\theta \, = \,{30^o}$   $3.$ $\frac{R}{H} = 4\sqrt 3 $
  $D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$   $4.$ $\frac{R}{H} = 4$

$K_i :$ initial kinetic energy

$K_h :$ kinetic energy at the highest point

  • A
    $A-1,\,\,B-2,\,\,C-3,\,\,D-4$
  • B
    $A-4,\,\,B-3,\,\,C-2,\,\,D-1$
  • $A-4,\,\,B-1,\,\,C-3,\,\,D-2$
  • D
    $A-3,\,\,B-2,\,\,C-4,\,\,D-1$

Answer

Correct option: C.
$A-4,\,\,B-1,\,\,C-3,\,\,D-2$
c
$1.$ $\frac{\mathrm{K}_{\mathrm{h}}}{\mathrm{K}_{\mathrm{i}}}=\frac{\frac{1}{2} \mathrm{m}(\mathrm{u} \cos \theta)^{2}}{\frac{1}{2} \mathrm{mu}^{2}}=\cos ^{2} \theta=\frac{1}{4} \Rightarrow \theta=60^{\circ}$

$2.$ $\frac{\mathrm{gT}^{2}}{\mathrm{R}}=\frac{\mathrm{g}\left(\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}}\right)^{2}}{\frac{\mathrm{u}^{2}}{\mathrm{g}} 2 \sin \theta \cos \theta}=2 \tan \theta=8$

$\Rightarrow \tan \theta=4 \Rightarrow \theta=\tan ^{-1}(4)$

$\frac{\mathrm{R}}{\mathrm{H}}=\frac{24^{2} \sin \theta \cos \theta}{\mathrm{g}} \times \frac{2 \mathrm{g}}{4^{2} \sin ^{2} \theta}=4 \cot \theta$

$ycot$ $\theta=y \sqrt{3}$

$\cot \theta=\sqrt{3}$

$\theta=30^{\circ}$

$ycot$ $\theta=y$

$\cot \theta=1$

$\theta=45^{\circ}$

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

Similar questions

Which is correct relation
A body of mass $10\, kg$ is moving with a constant velocity of $10 \,m/s$. When a constant force acts for $4 \,seconds$ on it, it moves with a velocity $2 \,m/sec$ in the opposite direction. The acceleration produced in it is...........$m/{\sec ^2}$
If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma $, the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ constant pressure $ p$, is
Two resistance are measured in $Ohm$ and is given as

$R_1 = 3 \Omega \pm 1\%$  and  $R_2 = 6 \Omega \pm 2\%$ When they are connected  in parallel, the percentage error in equivalent resistance is.......... $\%$

A ball of mass $( m )=0.5 \ kg$ is attached to the end of a string having length $(L)$ $=0.5 m$. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is $324 \ N$. The maximum possible value of angular velocity of ball (in radian/s) is
A thief stole a box full of valuable articles of weight $W$ and while carrying it on his back, he jumped down a wall of height $ ‘h’$ from the ground. Before he reached the ground he experienced a load of
In a playground there is a merry-go-round of mass $120\ kg$ and radius $4\ m$. The radius of gyration is $3\ m$. A child of mass $30\ kg$ runs at a speed of $5\ m/sec$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglect friction and find the angular velocity of the merry-go-round and child ......... $ rad/sec$.
If at temperature ${T_1} = 1000K,$ the wavelength is $1.4 \times {10^{ - 6}}m,$ then at ....... $K$  temperature the wavelength will be $2.8 \times {10^{ - 6}}m$
A tuning fork vibrates with frequency $256\, Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe . What is the length of the pipe? ... $cm$ (Speed of sound of air is $340\, ms^{-1}$)
A cyclic process $ABCD$ is shown in the $p-V$ diagram. Which of the following curves represents the same process if $BC \& DA$ are isothermal processes