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*Simulator*

**Previous Years AIEEE/JEE Mains Questions**

*l*and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

(1) $\frac{1}{2} \frac{l^{2} \omega^{2}}{g}$

(2) $\frac{1}{6} \frac{l^{2} \omega^{2}}{9}$

(3) $\frac{1}{3} \frac{l^{2} \omega^{2}}{9}$

( 4)$\frac{1}{6} \frac{l \omega}{g}$

**[AIEEE – 2009]**

**Sol.**()

in the $\mathrm{x}$ -y plane as shown in the figure. At a time $\mathrm{t}<\frac{\mathrm{v}_{0} \sin \theta}{\mathrm{g}},$ the angular momentum of the

particle is: Where $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ are unit vectors along $\mathrm{x}$, y and $\mathrm{z}$ -axis respectively.

(1) $\frac{1}{2} \mathrm{mg} \mathrm{v}_{0} \mathrm{t}^{2} \cos \theta \hat{\mathrm{i}}$

(2) $-\mathrm{mg} \mathrm{v}_{0} \mathrm{t}^{2} \cos \theta \hat{\mathrm{j}}$

(3) $\operatorname{mg} \mathrm{v}_{0}$ t $\cos \theta \hat{\mathrm{k}}$

(4)-\frac{1}{2} \operatorname{mg} v_{0} t^{2} \cos \theta \hat{k}

**[AIEEE-2010]**

**Sol.**(4)

(1) more than 6 but less than 9

(2) more than 9

(3) less than 3

(4) more than 3 but less than 6

**[AIEEE-2011]**

**Sol.**(4)

**[AIEEE-2011]**

**Sol.**(2)

(1) $\frac{\sqrt{3}}{2} \frac{\mathrm{mv}^{2}}{9}$

(2) zero

(3) $\frac{\mathrm{mv}^{3}}{\sqrt{2} \mathrm{g}}$

(4) $\frac{\sqrt{3}}{16} \frac{\mathrm{mv}^{3}}{\mathrm{g}}$

**[AIEEE-2011]**

**Sol.**(4)

(1) $\frac{\mathrm{r\omega}_{0}}{4}$

( 2)$\frac{\mathrm{r} \omega_{0}}{3}$

(3) $\frac{\mathrm{r} \omega_{0}}{2}$

(4) $\mathrm{r\omega}_{0}$

**[JEE Mains-2013]**

**Sol.**(3)

(1) Angular momentum changes in direction but not in magnitude

(2) Angular momentum changes both in direction and magnitude

(3) Angular momentum is conserved

(4) Angular momentum changes in magnitude but not in direction.

** [JEE Mains-2014]**

**Sol.**(1)

(1) $\frac{5 \mathrm{g}}{6}$ (2) g (3) $\frac{2 \mathrm{g}}{3}$ (4) $\frac{\mathrm{g}}{2}$

** [JEE Mains-2014]**

**Sol.**(4)

(1) $\frac{4 \mathrm{MR}^{2}}{9 \sqrt{3} \pi}$

(2) $\frac{4 \mathrm{MR}^{2}}{3 \sqrt{3 \pi}}$

(3) $\frac{\mathrm{MR}^{2}}{32 \sqrt{2} \pi}$

(4) $\frac{\mathrm{MR}^{2}}{16 \sqrt{2} \pi}$

**[JEE Mains-2015]**

**Sol.**(1)

Which of the following statement is false for the angular momentum $\overrightarrow{\mathrm{L}}$ about the origin ?

(1) $\overrightarrow{\mathrm{L}}=\frac{\mathrm{mv}}{\sqrt{2}} \mathrm{R} \hat{\mathrm{k}}$ when the particle is moving from $\mathrm{D}$ to $\mathrm{A}$

(2) $\overrightarrow{\mathrm{L}}=-\frac{\mathrm{mv}}{\sqrt{2}} \mathrm{R} \hat{\mathrm{k}}$ when the particle is moving from $\mathrm{A}$ to $\mathrm{B}$

(3) $\overrightarrow{\mathrm{L}}=\mathrm{mu}\left[\frac{\mathrm{R}}{\sqrt{2}}-\mathrm{a}\right] \hat{\mathrm{k}}$ when the particle is moving from $\mathrm{C}$ to $\mathrm{D}$

(4) $\overrightarrow{\mathrm{L}}=\mathrm{mv}\left[\frac{\mathrm{R}}{\sqrt{2}}+\mathrm{a}\right] \hat{\mathrm{k}}$ when the particle is moving from $\mathrm{B}$ to $\mathrm{C}$

**[JEE Mains-2016]**

**Sol.**(1,3)

(1) turn left and right alternately.

(2) turen left.

(3) turn right.

(4) go straight.

**[JEE Mains-2016]**

**Sol.**(2)

(1) 1

(2) $\frac{3}{\sqrt{2}}$

(3) $\sqrt{\frac{3}{2}}$

(4) $\frac{\sqrt{3}}{2}$

**[JEE Mains-2017]**

**Sol.**(3)

**[JEE Mains-2017]**

**Sol.**(3)

**[JEE Mains-2018]**

**Sol.**(4)

(1) $\frac{55}{2} \mathrm{MR}^{2}$

(2) $\frac{73}{2} \mathrm{MR}^{2}$

(3) $\frac{181}{2} \mathrm{MR}^{2}$

(4) $\frac{19}{2} \mathrm{MR}^{2}$

** [JEE Mains-2018]**

**Sol.**(3)

Please improve the writting of questions