1
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
A circular disc of radius R carries surface charge density
$$\sigma \left( r \right) = {\sigma _0}\left( {1 - {r \over R}} \right)$$, where $$\sigma$$0 is a constant and r is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is $$\phi$$0. Electric flux through another spherical surface of radius $${R \over 4}$$ and concentric with the disc is $$\phi$$. Then the ratio $${{{\phi _0}} \over \phi }$$ is ________.
2
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________.
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