The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $$1 \mathrm{~mm}$$. The main scale reading is $$2 \mathrm{~cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $$\mathrm{g}$$, the density of the sphere is:

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $$4^{\text {th }}$$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $$0.04 \mathrm{~mm}$$ then how many main scale divisions are there in $$1 \mathrm{~cm}$$ ?

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $$=49 \mathrm{~MSD} ; 20$$ divisions on main scale in each $$\mathrm{cm}$$

For mark on paper

$$\text { MSR }=8.45 \mathrm{~cm}, \mathrm{VC}=26$$

For mark on paper seen through slab

$$\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41$$

For powder particle on the top surface of the glass slab

$$\text { MSR }=4.05 \mathrm{~cm}, \mathrm{VC}=1$$

(MSR $$=$$ Main Scale Reading, VC = Vernier Coincidence)

Refractive index of the glass slab is :

To find the spring constant $$(k)$$ of a spring experimentally, a student commits $$2 \%$$ positive error in the measurement of time and $$1 \%$$ negative error in measurement of mass. The percentage error in determining value of $$k$$ is :