Consider a moving coil galvanometer (MCG) :
A : The torsional constant in moving coil galvanometer has dimensions [ML²T^–2]
B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C : If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles.
D : MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E : Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below :

Let's analyze each statement carefully:

(A) The torsional constant in a moving coil galvanometer has dimensions [ML²T⁻²].

The torsional constant ($k$) relates the torque $\tau$ and angular displacement $\theta$: $$\tau = k \theta$$

Torque has the dimension [ML²T⁻²], and since $\theta$ is dimensionless, $k$ must also have the same dimension.

So, the given dimension is correct.

(B) Increasing the current sensitivity may not necessarily increase the voltage sensitivity. 

Current sensitivity ($S_I$) is given by: $$S_I = \frac{NAB}{k}$$ where $N$ = number of turns, $A$ = area, $B$ = magnetic field, $k$ = torsional constant.

Voltage sensitivity ($S_V$) is given by: $$S_V = \frac{S_I}{R} = \frac{NAB}{kR}$$ where $R$ is the resistance of the coil.

If $R$ also increases when $S_I$ increases, then $S_V$ may not necessarily increase.

So, this statement is correct.

(C) If we increase the number of turns (N) to its double (2N), then the voltage sensitivity doubles. 

Voltage sensitivity: $$S_V = \frac{NAB}{kR}$$

If $N$ is doubled ($2N$), then $S_V$ doubles only if $R$ remains constant.

However, doubling $N$ also increases the resistance $R$ (since $R \propto N$), which may offset the increase.

Hence, voltage sensitivity may not necessarily double, making this statement false.

(D) MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with the galvanometer. 

Ammeter conversion requires a small shunt resistance, so that most of the current bypasses the galvanometer.

A large shunt resistance would not allow enough current to bypass, leading to incorrect measurements.

So, this statement is false.

(E) Current sensitivity of MCG depends inversely on the number of turns of the coil. 

Current sensitivity is given by: $$S_I = \frac{NAB}{k}$$

Since $S_I \propto N$, increasing $N$ increases $S_I$.

The statement claims an inverse relationship, which is incorrect.

Hence, this statement is false.

Final Answer:

✔ Correct statements: (A) and (B)
✖ Incorrect statements: (C), (D), (E)

So, the correct option is (A) and (B).