MEDIUM
JEE Main
IMPORTANT
Earn 100

When a rubber ball is taken to a depth of _______ m in deep sea, its volume decreases by 0.5%
(The bulk modulus of rubber =9.8×108 N m-2 Density of sea water =103 kg m-3,g=9.8 m s-2)

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Important Questions on Properties of Solid and Liquid

MEDIUM
JEE Main
IMPORTANT
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50×103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column.
[use Y=2.0×1011 Pa, g=9.8 m s-2]
MEDIUM
JEE Main
IMPORTANT

A student determined Young's Modulus of elasticity using the formula Y=MgL34bd3δ. The value of g is taken to be 9.8 m s-2 without any significant error, his observations are as following.

Physical Quantity

Least count of the Equipment used for measurement

Observed Value
Mass (M) 1 g 2 kg
Length of bar (L) 1 mm 1 m
Breadth of bar (b) 0.1 mm 4 cm
Thickness of bar  (d) 0.01 mm 0.4 cm
Depression (δ) 0.01 mm 5 mm

Then the fractional error in the measurement of Y is :

MEDIUM
JEE Main
IMPORTANT
The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are 1 and 2, respectively. The actual length of the metal wire is:
MEDIUM
JEE Main
IMPORTANT
Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is
MEDIUM
JEE Main
IMPORTANT
Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is:
HARD
JEE Main
IMPORTANT
Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:
HARD
JEE Main
IMPORTANT

A light cylindrical vessel is kept on a horizontal surface. Area of the base is A. A hole of cross-sectional area a is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is

Question Image

HARD
JEE Main
IMPORTANT
A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10-6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is m s-1. (Young's modulus of rubber =0.5×109 N m-2)