If a composite physical quantity in terms of moment of inertia I, force F, velocity v, work W and length L is defined as `Q = (iFv^2)/(WL^3)`, find dimensions of Q and identify it.

KE of a rotating body is given by 1/2 I omega^2 ,where l is moment of inertia and omega is nagular velocity of the body.Find the dimensions of I.

Define the term work function of a metal. The threshold frequency of a metal is 2f_0 is incident on the metal plate, the maximum velocity of electrons emitted is v_1 , when the frequency of the incident radiation is increased of 5f_0 the maximum velocity of electrons emitted is v_2 . Find the ratio of v_1 to v_2 .

Define the term work function of a metal. The threshold frequency of a metal is f_0 when the light of frequency 2f_0 is incident on the metal plate, the maximum velocity of electrons emitted is v_1 , when the frequency of the incident radiation is increased to 5f_0 , the maximum velocity of electrons emitted is v_2 . Find the ratio of v_1 and v_2 .

Find the moment of vec F about point (2, -1, 3), where force vec F=3 hat i+2 hat j-4 hat k is acting on point (1, -1, 2).

Point masses m_1 and m_2 are placed at the opposite ends of a rigid rod of length L, and nelgligible mass. The rod is to be set rotating about an axis perpendicular to it. Find the position on this rod through which the axis should pass in order that the work required to set the rod rotating with angular velocity omega_0 should be minimum.

There is another useful system of units, besides the SI/MKS. A system, called the cgs system. In this system Coulumb's law is given by vecF = (Qq)/(r^2) hatr where the distance r is measured in cm (=10^(-2) m) , F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1es unit of charge = 1/[3] xx 10^(-9) C . The number [3] actually arises the speed of light in vacuum which now taken to be exactly given by c = 2.99792458 xx 10^8 m/s . An approximate value of c then is c = [3] xx 10^8 m/s . Show that the Coulomb law in cgs units yields. 1 esu of charge = 1 (dy )^(1/2) cm . obtain the dimension of units of charge in terms of mass M, length L and time T. show that it is given in terms of fractional powers of M and L.

Forces 2hat(i)+hat(j), 2hat(i)-3hat(j)+6hat(k) and hat(i)+2hat(j)-hat(k) act at a point P, with position vector 4hat(i)-3hat(j)-hat(k) . Find the moment of the resultant of these force about the point Q whose position vector is 6hat(i)+hat(j)-3hat(k) .

Two long parallel wires carrying current 2.5 amperes and I ampere in the same Idirection ( directed into the plane of the paper) are held at P and Q respectively such that they are perpendicular to the plane of paper. The points P and Q are located at a distance of 5 metres and 2 metres respectively from a collinear point R ( see figure) An electron moving with a velocity of 4xx10^(5) m//s along the positive x- direction experiences a force of magnitude 3.2xx10^(-20) N at the point R. Find the value of I.

A charge Q located at a point rarrr is in equilibrium under the combined electric field of three charges q_1, q_2 and q_3 if the charges q_1, q_2 are located at the points rarrr_1 and rarrr_2 respectively, find the direction of the force on Q, due to q_3 , in term of q_1,q_2,q_3 rarrr, rarrr_1, and rarrr_2