A vertical cylinder of height 100cm contians air at a constant temperatur. The top is closed by a frictionless light postpn. The atmospheric pressure pver the piston.
The velocity of a particle is zero at t=0 (A) The accelerationat t=0 must be zero (B) the acceleration at t=0 maybet zero (C) If the acceleratin is zero from t=0 to t=10 s, the speed is also zero in this interval. (D) If the speed is zer4o from t=0 to t=10 s the acceleration is zero in this interval.
A car of maas M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a. (A) The acceleration of the car is towards the centre of the path (B) The magnitude the frictional force on the car is greater than \(\frac{{{m}{v}^{{2}}}}{{r}}\). (C) The friction coefficient between the ground and the car is not less than \(\frac{{a}}{{g}}\). (D) The friction coefficient between the ground and the car is \(\mu=\frac{{{\tan}^{{-{{1}}}}{v}^{{2}}}}{{r}}{g}\)
One end of a wire 2m long and 0.2 cm^2 in cross section is fixed in a ceilign and a load of 4.8 kg is attached to the free end. Find the extension of the wire. Young modulus of steel \(={2.0}\times{10}^{{11}}{N}{m}^{{-{{2}}}}\). Take \({g}={10}{m}{s}^{{-{{2}}}}\).
Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given frequencies ? (c) Which overtones are these frequencies ? (d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this string ?
Assume that each atom in a copper wire contributes one free electron. Estimate the numberof free electrons in a cpper wire having a mass of 6.4g (take the atomic weight of copper ot be 64g \({m}{o}{l}^{{-{1}}}.\)
An inductor coil of resistance \({10}\Omega\) and inductance 120 mH is connected across a battery of emf 6 V and internal resistance \({2}\Omega\). Find the charge which flows through the inductor in (a) 10 ms, (b) 20ms and (c ) 100ms after the connections are made.