Other Physics · JEE Advanced previous year questions

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height $y$ (in m) of the elevator, from the ground, with time $t$ (in s) is given by $y=8\left[1+\sin \left(\frac{2\pi t}{T}\right)\right]$, where $T=40\pi$ s. Taking acceleration due to gravity, $g=10m/{\mathrm{s}}^2$, the maximum variation of the object’s weight (in N) as observed in the experiment is ____

Consider a star of mass $m_2$ kg revolving in a circular orbit around another star of mass $m_1$ kg with $m_1\gg m_2$. The heavier star slowly acquires mass from the lighter star at a constant rate of $\gamma$ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is $r$, then its relative rate of change $\frac{1}{r}\frac{dr}{dt}$ (in ${\mathrm{s}}^{-1}$) is given by:

1. A.$-\frac{3\gamma }{2m_2}$
2. B.$-\frac{2\gamma }{m_2}$
3. C.$-\frac{2\gamma }{m_1}$
4. D.$-\frac{3\gamma }{2m_1}$

A ball is thrown from the location $(x_0,y_0)=(0,0)$ of a horizontal playground with an initial speed $v_0$ at an angle ${\theta }_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $(x_1,y_1)=(L,0)$. The stone is thrown at an angle $(180-{\theta }_1)$ from the $+x$-direction with a suitable initial speed. For a fixed $v_0$, when $({\theta }_0,{\theta }_1)=(45^{\circ },45^{\circ })$, the stone hits the ball after time $T_1$, and when $({\theta }_0,{\theta }_1)=(60^{\circ },30^{\circ })$, it hits the ball after time $T_2$. In such a case, $(T_1/T_2{)}^2$ is ____.

A particle of mass $m$ is moving in the $xy$-plane such that its velocity at a point $(x,y)$ is given as $\vec{v}=\alpha (y\hat{x}+2x\hat{y})$, where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

1. A.$\vec{F}=2m{\alpha }^2(x\hat{x}+y\hat{y})$
2. B.$\vec{F}=m{\alpha }^2(y\hat{x}+2x\hat{y})$
3. C.$\vec{F}=2m{\alpha }^2(y\hat{x}+x\hat{y})$
4. D.$\vec{F}=m{\alpha }^2(x\hat{x}+2y\hat{y})$