A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to :
(1 HP = 746 W, g = 10 ms^-2)

A long solenoid of radius R carries a time (t) - dependent current
I(t)=I₀t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 $$ \le $$ t $$ \le $$ 1, the induced current (I_R) and the induced EMF(V_R) in the ring change as :

Visible light of wavelength 6000 $$ \times $$ 10^-8 cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60^o from the central maximum. If the first minimum is produced at $$\theta $$₁, then $$\theta $$₁, is close to :

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90 ms^-1. If the Young's modulus of wire is 16 $$ \times $$ 10¹¹ Nm^-2, the extension of wire over its natural length is :