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JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1
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A particle of mass $1 \mathrm{~kg}$ is subjected to a force which depends on the position as $\vec{F}=$ $-k(x \hat{\imath}+y \hat{\jmath}) \mathrm{kg}\, \mathrm{m} \mathrm{s}^{-2}$ with $k=1 \mathrm{~kg} \mathrm{~s}^{-2}$. At time $t=0$, the particle's position $\vec{r}=$ $\left(\frac{1}{\sqrt{2}} \hat{\imath}+\sqrt{2} \hat{\jmath}\right) m$ and its velocity $\vec{v}=\left(-\sqrt{2} \hat{\imath}+\sqrt{2} \hat{\jmath}+\frac{2}{\pi} \hat{k}\right) m s^{-1}$. Let $v_{x}$ and $v_{y}$ denote the $x$ and the $y$ components of the particle's velocity, respectively. Ignore gravity. When $z=0.5 \mathrm{~m}$, the value of $\left(x v_{y}-y v_{x}\right)$ is __________ $m^{2} s^{-1}$.
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2
JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1
Change Language

On a frictionless horizontal plane, a bob of mass $m=0.1 \mathrm{~kg}$ is attached to a spring with natural length $l_{0}=0.1 \mathrm{~m}$. The spring constant is $k_{1}=0.009 \,\mathrm{Nm}^{-1}$ when the length of the spring $l>l_{0}$ and is $k_{2}=0.016 \,\mathrm{Nm}^{-1}$ when $l < l_{0}$. Initially the bob is released from $l=$ $0.15 \mathrm{~m}$. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) s$, then the integer closest to $n$ is __________.

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3
IIT-JEE 2010 Paper 1 Offline
Numerical
+3
-0
A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its crosssectional area is 4.9 $$ \times $$ 10-7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s−1. If the Young’s modulus of the material of the wire is n $$ \times $$ 109 Nm-2, the value of n is
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