Units and Measu...

The dimension[ M L T] may correspond to 

A pressure $$O$$, velocity of light $$C$$ and acceleration due to gravity g are chosen as fundamental units, then dimensional formula of mass is 

The dimension of magnetic field in $$M,L,T$$ and $$C$$ (Colulomb) is given as

What is dimension of $$ \frac {d^2x}{dy^2} $$ where x is pressure and y is energy incident over unit area in unit time of a surface? 

Four particles of mass $$m_1=2$$m, $$m_2=4$$m, $$m_3=$$m and $$m_4$$ are placed at four corners of a square. What should be the value of $$m_4$$ so that the centre of mass of all the four particles are exactly at the centre of the square?

The equation of state for a real gas such as hydrogen, oxygen, etc. is called the Van der Waal's equation which reads 
$$\left(P+\dfrac{a}{V^{2}}\right)(V-b)=nRT$$
Where a and b are constant of a gas. the dimensional formula of constant a is:

The accuracy in the measurement of the diameter of hydrogen atom as 1.06 x $$10^{-10}$$ m is

Figure shows a weighing machine kept in a lift is moving upwards with acceleration of $$5$$ $$m/s^2$$. A block is kept on the weighing machine. Upper surface of block is attached with a spring balance. Reading shown by weighing machine and spring balance is $$15$$ kg and $$45$$ kg respectively.
Answer the following question. Assume that the weighing machine can measure weight by having negligible deformation due to block, while the spring balance requires larger expansion(take $$g=10m/s^2$$).
Mass of the object in kg and the normal force acting on the block due to weighing machine are?

A uniform rod of mass M and length L leans against a frictionless wall, with quarter of its length hanging over a corner as shown. Friction at corner is sufficient to keep the rod at rest. Then the ratio of magnitude of normal reaction on rod by wall and the magnitude of normal reaction on rod by corner is?

$$V$$ is the volume of a liquid flowing per second through a capillary tube of length $$l$$ and radius $$r$$, under a pressure difference $$(p)$$. If the velocity $$(v)$$, mass $$(M)$$ and time $$(T)$$ are taken as the fundamental quantities, then the dimensional formula for $$\eta$$ in the relation $$V = \dfrac {\pi p r^{4}}{8\eta l}$$ is