$(a)\ I_{xR}/I_{xS} <1;\ (b)\ I_{yR}/I_{yS} >1; \ (c)\ I_{zR}/I_{zS} >1$
$\mathrm{I}_{\mathrm{XR}}=\frac{\mathrm{Mb}^{2}}{12}, \mathrm{I}_{\mathrm{YR}}=\frac{\mathrm{Ma}^{2}}{12}, \mathrm{I}_{\mathrm{ZR}}=\frac{\mathrm{M}\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)}{12}$
$\mathrm{I}_{\mathrm{XS}}=\frac{\mathrm{Mc}^{2}}{12}, \mathrm{I}_{\mathrm{YS}}=\frac{\mathrm{Mc}^{2}}{12}, \mathrm{I}_{\mathrm{zs}}=\frac{\mathrm{Mc}^{2}}{6}$
$\frac{\mathrm{I}_{\mathrm{ZR}}}{\mathrm{I}_{\mathrm{ZS}}}=\frac{1}{2}\left(\left(\frac{\mathrm{a}}{\mathrm{c}}\right)^{2}+\left(\frac{\mathrm{b}}{\mathrm{c}}\right)^{2}\right)$
$=\frac{1}{2}\left(\left(\frac{\mathrm{a}}{\mathrm{c}}\right)^{2}+\left(\frac{\mathrm{c}}{\mathrm{a}}\right)^{2}\right)$
$\frac{I_{\mathbb{Z R}}}{I_{Z S}}>1$
$x+\frac{1}{x}>2$ if $x>0$
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|
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
If $v_1 = v_2$ and $\theta _1 > \theta _2$, then choose the incorrect statement