JEE PYQ: Units & Measurements - Question ID 2c8642042b5c (JEE Main 2014)

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text {th }}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

Dimensions of universal gravitational constant ($G$) in terms of Planck's constant ($h$), distance ($L$), mass ($M$) and time ($T$) are _______.

The time period of a simple harmonic oscillator is $T = 2\pi \sqrt{\frac{k}{m}}$. Measured value of mass $(m)$ of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant $(k)$ is ________%.

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, $4{ }^{\text {th }}$ mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and $5^{\text {th }}$ division of vernier scale coincides with a main scale division. Measured length of cylinder is $\_\_\_\_$ mm.

(Least count of Vernier calliper $=0.1 \mathrm{~mm}$ )