`1 ( mu m)/(mg)=________(Mm)/(ng)`

45mm = _________ m

1 kg m//s^(2) =___gm- mm//s^(2)

Figure-2.85 shows a block B of mass m, cart C of mass M, and the coefficient of static between the block and the cart is mu . Neglect frictional between wheels and axles and the rotational effects of the wheels. Determine the minimum value of F which must be applied on B such that it will not slide. [(mg)/(mu)(1+(m)/(M))]

Assertion : A double convex lens (mu=1.5) has focal length 10 cm . When the lens is immersed in water (mu=4//3) its focal length becomes 40 cm . Reason : (1)/(f)=(mu_(1)-mu_(m))/(mu_(m))((1)/(R_(1))-(1)/(R_(2)))

Time taken by the sunlight to pass through a window made of glass of 5 mm thickness is __________ s. (mu_("glass")=1.5)

For a two body oscillator system, prove the relation, T = 2pi sqrt((mu)/(k)) where, mu = (m_(1)m_(2))/(m_(1) + (m_(2))) = reduced mass.

Show that the force of attraction between two short magnets of moment m and m' with their centres d distance apart and their axes in the same direction along the same lines is (mu_(0))/(4pi) (6mm')/(d^(4))

Two blocks of masses m_(1) and m_(2) kept touching each other on an inclined plane of inclination a with the horizontal. Show that (i) theforce of interaction between the blocks is ((mu_(1)-mu_(2))m_(1)m_(2)gcosalpha)/((m_(1)+m_(2))) and (ii) the minimum value of alpha at which the blocks just start sliding is a = tan^(-1).(mu_(1)m_(1)+mu_(2)m_(2))/(m_(1)+m_(2)) . Where mu_(1) and mu_(2) are the coefficients of friction between the block m_(1) and the inclined plane and between the block m_(2) and the inclinedplane respectively.

Find the accelerations of blocks A and B for the following cases. (A) mu_(1)=0 " and "mu_(2)=0.1" (P)" a_(A)=a_(B)=9.5m//s^(2) (B) mu_(2)=0 " and "mu_(1)=0.1 " (Q)"a_(A)=9m//s^(2), a_(B)=10m//s^(2) (C) mu_(1)=0.1 " and "mu_(2)=1.0 " (R)"a_(A)=a_(B)=g=10m//s^(2) (D) mu_(1)=1.0 " and "mu_(2)=0.1 " (S)" a_(A)=1, a_(B)=9m//s^(2)

A spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring an eleongation less than (2 mu mg)/(K) but more than (mu mg)/(K) and released. The correct statement is :