An experiment was conducted to measure the velocity of water splash when a cat passes over a water layer on the road. It is found that velocity depends on the weight of car, power delivered by its engine and thickness of water layer. The velocity of splash was found to be $$3$$ $$m/s$$ when a cat weighing $$1000$$ N passes over a layer of thickness $$3$$ mm and its engine is supplying a power of $$800$$ kW. Find the velocity (in$$ $$m/s) of splash when car weighing $$500$$ N passes over a layer of thickness $$4mm$$ and its engine is supplying a power of just $$400$$ kW.

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Infinity Learn · Accepted Answer

From dimensional analysis, velocity of water splash v∝kFaPbtc⇒    $$M0L1T$$−$$1=MLT$$−$$2aML2T$$−$$3bLc$$∴    $$a+b=0$$    $$a+2b+c=1$$    −$$2a$$−$$3b=$$−$$1$$∴      $$a=$$−$$1$$,$$b=1$$ and $$c=0Hence$$ v∝PF∴ $$v1v2=F1$$−$$1P1F2$$−$$1P2$$⇒$$v2=v1P2F1P1F2=3$$×$$400$$×$$1000800$$×$$500=3m/s$$

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