A disc arranged in a vertical plane has two groves of same length directed along the vertical chord $AB$ and $CD$ as shown in the fig. The same particles slide down along $AB$ and $CD$. The ratio of the time $t_{AB}/t_{CD}$ is then

Q. A disc arranged in a vertical plane has several grooves directed along the chords drawn from a point A (topmost point) as shown in the figure. Several bodies begin to slide down the respective grooves from A simultaneously. The ratio of their times of slide will be: (neglect friction and air resistance)

Q.

A, B, C, D are the points in a vertical line, the lengths AB=BC=CD . If the body Falls from rest at A , prove that the times of describing AB, BC, CD are as 1:√2-√1:√3-√2 .

Q.

In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ?

(a) $\frac{1}{2}AB$

(b) $\frac{1}{2}CD$

(c) $\frac{1}{2}(AB+CD)$

(d) $\frac{1}{2}(AB-CD)$

Q. AB and CD are two parallel conductors kept $1$m apart and connected by a resistance R of $6\Omega$ as shown in figure. They are placed in a magnetic field B$=3\times {10}^{-2}$T which is perpendicular to the plane of the conductors and directed into the paper. A wire MN is placed over AB and CD and then made to slide with a velocity $2m{s}^{-1}$.(Neglect the resistance of AB, CD, and MN). Calculate the induced current flowing through the resistor R.