In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

A man is 48m behind a bus which is at rest. The bus starts accelerating at the rate of 1m//s^(2) , at the same time the man starts running with uniform velocity of 10 m/s. What is the minimum time in which the man catches the bus ?

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is 2xx10^9 N m^-2 . What should be the minimum radius of the wire used if it is not to break?

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below. Show that it follows a pseudo first order reaction, as the concentration of water remains nearly constant (55 mol L^(-1)), during the course of the reaction. What is the value of k in this equation? Rate =k'[CH_(3) COOCH_(3) ][H_(2)O]

A heating element using nichrome connected to a 230V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8A. What is the steady temperture of the heating element if the heating the room temperature is 27.0^(@)C ? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 xx 10^(-4) .^(@)C^(-1) .