An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $$x=+2~\mathrm{m}$$, its velocity is $$\mathrm{ - 4\widehat j}$$ m/s. The object's velocity (v) and acceleration (a) at $$x=-2~\mathrm{m}$$ will be

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

A fully loaded boeing aircraft has a mass of $$5.4\times10^5$$ kg. Its total wing area is 500 m$$^2$$. It is in level flight with a speed of 1080 km/h. If the density of air $$\rho$$ is 1.2 kg m$$^{-3}$$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($$\mathrm{g=10~m/s^2}$$)