brilliant tutorials physics questions..........

1)if Y represents acceleration and X momentum,then the dimension of (d²Y / dX² )^1/2 is ???

A) M^-1 L^-1/2 T⁰
B) M L^1/2 T^-1/2
C) M^-1 L^1/2 T^1/2
D)M⁰ L^1/2 T^1/2

2)the position vector of a particle is given by r=r₀(1-αt)t ,where t is the time and α is a scalar constant and r₀ is a constant vector. Then

A)distance covered in forward journey is |r₀| /(2α)
B)distance covered in backward journey is |r₀| /(4α)
c)total distance covered is |r₀| / (2α)
D)the particle will come to starting point at t=1/ (2α)

3)the radii of the front and rear wheels of a carriage are a and b respectively and c is the distance between the axles. A dust particle driven from the highest point of the rear wheel is observed to settle on the the highest point of the front wheel. The velocity of the particle with respect to the carriage is

a)√g √(c+b-a)(c+a-b) / √4(b+a)

b)√g √(c+b+a)(a+b-c) / √4(b-a)

c)√g √(c+b+a)(c+a-b) / √4(b-a)

d)√g √(c+b-a)(c+a-b) / √4(b-a)