Two balls \(A\) and \(B\) are placed at the top of \(180 \,m\) tall tower. Ball \(A\) is released from the top at \(t =0 \,s\). Ball \(B\) is thrown vertically down with an initial velocity \(u\)' at \(t=2\, s\). After a certain time, both balls meet \(100 \,m\) above the ground. Find the value of \(u\) in ............... \(ms ^{-1}\). [use \(g =10 \,ms ^{-2}\) ]

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction)

The amount of work done to break a big water drop of radius ' \(R\) ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be

The amplitude of a damped oscillator decreases to \(0.9\) times its original magnitude in \(5\ s\). In another \(10\ s\) it will decrease to \(\alpha \) times its original magnitude, where  \(\alpha \) equals

A resistor dissipates \(192\, {J}\) of energy in \(1\, {s}\) when a current of \(4\, {A}\) is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in \(5 \,{s}\) in \(.....\,J.\)

A block of mass \(m = 10\,kg\) rests on a horizontal table. The coefficient of friction between the block and the table is \(0.05.\) When hit by a bullet of mass \(50\,g\) moving with speed \(v,\) that gets embedded in it, the block moves and comes to stop after moving a distance of \(2\,m\) on the table. If a freely falling object were to acquire speed \(\frac {v}{10}\) after being dropped from height \(H,\) then neglecting energy losses and taking \(g = 10\,ms^{-2},\) the value of \(H\) is close to ................. \(\mathrm{km}\)

The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) The escape velocities of planet \(A\) and \(B\) are same. But \(A\) and \(B\) are of unequal mass. Reason \(R :\) The product of their mass and radius must be same, \(M _{1} R _{1}= M _{2} R _{2}\) In the light of the above statements, choose the most appropriate answer from the options given below

At \(t=0\), a body of mass \(100\) g starts moving under the influence of a force \((5\hat{i}+10\hat{j})\) N. After \(2\) s its position is \((2x\hat{i}+5y\hat{j})\) m. The ratio \(x:y\) is ______.

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point \(A\) is \(10 \mathrm{~m} / \mathrm{s}\). The ratio of its kinetic energies at point \(B\) and \(C\) is :

(Take acceleration due to gravity as \(10 \mathrm{~m} / \mathrm{s}^2\) )

A \(2\,V\) battery is connected across \(AB\) as shown in the figure. The value of the current supplied by the battery when in one case battery's positive terminal is connected to \(A\) and in other case when positive terminal of battery is connected to \(B\) will respectively be

Two wires each of radius \(0.2\,cm\) and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is \(.........\times 10^{-6}\,m\). [Young's modulus for steel \(=2 \times 10^{11}\,Nm ^{-2}\) and \(g =10\,ms ^{-2}\) ]