A glass flask having mass 390 g and an interior volume of 500 floats on water when it is less than half filled with water. The density of material of the flask is
1
0.8 g/cc
2
2.8 g/cc
3
1.8 g/cc
4
0.28 g/cc
Official Solution
Correct Option: (2)
Step 1: Analysis
When half filled, it floats fully submerged: Mass of flask + mass of water in it = Total displacement weight.
(outer volume). Step 2: Material Volume
Volume of material = Outer volume - Inner volume = . Step 3: Density
Density . Final Answer: (B)
02
PYQ 2015
medium
physicsID: met-2015
A uniform rod of length 2 m, specific gravity 0.5 and mass 2 kg is hinged at one end to the bottom of a tank of water (specific gravity = 1.0) filled upto a height of 1 m as shown in the figure. Taking the case , the force exerted by the hinge on the rod is
1
10.2 N upwards
2
4.2 N downwards
3
8.3 N downwards
4
6.2 N upwards
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept:
Take torques about the hinge. The length submerged is . Upthrust acts at mid-point of submerged length. Weight acts at centre of rod.
Step 2: Detailed Explanation:
From torque balance: . Solving gives . At : Upthrust N. Weight N. Vertical equilibrium: N. Negative means downward.
Hinge force N downwards.
Step 3: Final Answer:
Force exerted by hinge N downwards.
03
PYQ 2015
medium
physicsID: met-2015
A small block of wood of specific gravity 0.5 is submerged at a depth of 1.2 m in a vessel filled with water. The vessel is accelerated upwards with an acceleration . Time taken by the block to reach the surface, if it is released with zero initial velocity is
1
0.6 s
2
0.4 s
3
1.2 s
4
1 s
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept:
In an accelerating vessel, the effective gravity is . Upthrust , weight . Net upward acceleration of block relative to vessel.
Step 2: Detailed Explanation:
Block acceleration in ground frame:
Relative acceleration m/s . Wait, relative to vessel: . Hmm, let me redo: net acc of block (upward) in ground frame. Relative to vessel (acc upward): . Using : s.
