The angular displacement `(theta)` of the blades of a ceiling fan, when the fan is switched on at t=0, is shown in figure. The average angular velocity of the fan blades during the first 8 seconds will be
The velocity-time graph of a car moving along a straight road is shown in figure. The average velocity of the car in first 25 seconds is
The velocity-time graph of a car moving along a straight road is shown in figure. The average velocity of the car is first 25 seconds is
In space of horizontal EF (E = (mg)//q) exist as shown in figure and a mass m is released at the end of a light rod. If mass m is releases from the position shown in figure find the angular velocity of the rod when it passes through the bottom most position .
A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10m//s . The wavelength of the wave is 0.5m and its amplitude is 10cm . At a particular time t , the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5cm is -
A uniform thin cylindrical disk of mass M and radius R is attaached to two identical massless springs of spring constatn k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. the unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity vecV_0 = vacV_0hati. The coefficinet of friction is mu. The centre of mass of the disk undergoes simple harmonic motion with angular frequency omega equal to -
A uniform thin cylindrical disk of mass M and radius R is attaached to two identical massless springs of spring constatn k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. the unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity vecV_0 = vacV_0hati. The coefficinet of friction is mu. The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is.
A line charge lambda per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light nonconducting spokes and is free to rotate without friction about its axis as per figure. A uniform magnetic field extends over a circular region within the rim. It is given by, B=-B_0 k ( r le a , a lt R) =0 (otherwise) What is the angular velocity of the wheel after the field is suddenly switched off ?
A hemisphere of radius R and mass 4 m is free to slide with its base on a smooth horizontal table . A particle of mass m is placed on the top of the hemisphere . The angular velocity of the particle relative to centre of hemisphere at an angular displacement theta when velocity of hemisphere has become v is
