The Nucleus — Physics STD 11 Science — Question

If several forces act on a particle, the total torque on the particle may be obtained by first finding the resultant force and then taking torque of this resultant. Prove this. Is this result valid for the forces acting on different particles of a body in such a way that their lines of action intersect at a common point?

Two wires of different densities but same area of crosssection are soldered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.

A particle is projected vertically upwards from the surface of Earth of radius R with a kinetic energy equal to half of the minimum value needed for it to escape. Find the height to which it rises above the surface of Earth.

Some measurements are taken for the period of oscillations of a simple pendulum. In successive measurements, the readings turn out to be 2.63s, 2.56s, 2.42s, 2.71s and 2.80s. Calculate the absolute errors, relative error and percentage error.

Read each statement below carefully and state with reason, if it is true or false :
(a) The magnitude of a vector is always a scalar,
(b) each component of a vector is always a scalar,
(c) the total path length is always equal to the magnitude of the displacement vector of a particle.
(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.

A woman starts from her home at 8.00 a.m., walks with a speed of 5km/ hr on a straight road upto her office 5km away stays at the office upto 4 p.m., and returns home by an auto with a speed of 25km/ hr. Choose suitable scales, and plot the x-t graph of her motion.

A square plate of mass 120g and edge 5.0cm rotates about one of the edges. If it has a uniform angular acceleration of 0.2rad/s², what torque acts on the plate?

A monkey of mass 15kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of 1m/s², how much force should it apply to the rope? If the rope is 5m long and the monkey starts from rest, how much time will it take to reach the ceiling?