The acceleration-time graph of a particle moving in a straight line is shown in the figure. If the initial velocity of the particle is zero then the velocity-time graph of the particle will be
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The position vector of a particle of mass $$\mathrm{m}$$ moving with a constant velocity $$\vec{v}$$ is given by $$\vec{r}=x(t) \hat{i}+b \hat{j}$$, where $$\mathrm{b}$$ is a constant. At an instant, $$\vec{r}$$ makes an angle $$\theta$$ with the $$x$$-axis as shown in the figure. The variation of the angular momentum of the particle about the origin with $$\theta$$ will be
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The position of the centre of mass of the uniform plate as shown in the figure is
In a series LCR circuit, the rms voltage across the resistor and the capacitor are $$30 \mathrm{~V}$$ and $$90 \mathrm{~V}$$ respectively. If the applied voltage is $$50 \sqrt{2} \sin \omega t$$, then the peak voltage across the inductor is