It is a common observation that rain clouds can be at about a kilometre altitude above the ground.

(a) If a rain drop falls from such a height freely under gravity, what will be its speed? Also calculate in km/h. (g = 10m/s2)

(b) A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.

(c) Estimate the time required to flatten the drop.

(d) Rate of change of momentum is force. Estimate how much force such a drop would exert on you.

(e) Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5 cm. (Assume that umbrella is circular and has a diameter of 1m and cloth is not pierced through !!)

Two trains 101 m and 99 m in length are running in opposite direction with velocities 54 km/h and 36 km/h. In what time they will completely cross each other?

Distance travelled by a particle starting form rest and moving with an acceleration of 4/3ms^-2 in the second is

Match List – I with List – II :

List – I                                                                               List – II

(a) h (Planck’s constant)                                               (i) $\left[ML{T}^{-1}\right]$  

(b) E (kinetic energy)                                                     (ii) $\left[M{L}^2{T}^{-1}\right]$        

(c) V (electric potential)                                                (iii) $\left[M{L}^2{T}^{-2}\right]$  

(d) P (linear momentum)                                             (iv) $\left[M{L}^2{I}^{-1}{T}^{-3}\right]$  

Choose the correct answer from the options given below:

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be:

A vehicle travels half the distance with speed  $\mathrm{v}$ and the remaining distance with speed $2\mathrm{v}$ . Its average speed is:
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