Four identical point masses $'m'$ joined by light string of length $'l'$ arrange such that they form square frame. Centre of table is coincide with centre of arrangment. If arrangement rotate with constant angular velocity $'\omega '$ , find out tension in each string

- A
$\frac{{m{\omega ^2}l}}{4}$

- B
$m{\omega ^2}l/2$

- C
$m{\omega ^2}l/\sqrt 2 $

- D
$m{\omega ^2}l$

A train is running at $20 \,m / s$ on a railway line with radius of curvature $40,000$ metres. The distance between the two rails is $1.5$ metres. For safe running of train the elevation of outer rail over the inner rail is ......$mm$ $\left( g =10 \,m / s ^2\right)$

A particle has initial velocity $10\,\, m/s$. It moves due to constant retarding force along the line of velocity which produces a retardation of $5\,\, m/s^2$. Then

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- [AIPMT 1999]

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is $v_0$, then the ratio of tensions in the three sections of the string is

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