Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross sectional area 10⁻⁶ m². The breaking stress of the wire is 7 × 10⁶ N/m². The block is placed in beaker of base area 200 cm² and initially i.e., at t = 0, the top surface of water and the block coincide. There is a pump at the bottom corner which ejects 2 cm³ of water per second. If the time at which the wire will break is 20 × z seconds, find z.
Physics · Mixed Chapter
JEE Mains

Question

Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross sectional area 10⁻⁶ m². The breaking stress of the wire is 7 × 10⁶ N/m². The block is placed in beaker of base area 200 cm² and initially i.e., at t = 0, the top surface of water and the block coincide. There is a pump at the bottom corner which ejects 2 cm³ of water per second. If the time at which the wire will break is 20 × z seconds, find z.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Block volume=(0.1)³=10⁻³ m³; mass=1.5×10³×10⁻³=1.5 kg. With g≈10 m s⁻², weight=15 N. Step 2: Maximum sustainable tension=stress×wire area=7×10⁶×10⁻⁶=7 N. At breaking, buoyancy=15−7=8 N, so the block is immersed to depth 8 cm (initially 10 cm). Step 3: Water level must fall by 2 cm. Since the block occupies 100 cm², effective water-surface area is (200−100)=100 cm² during this fall. Pumped volume=100×2=200 cm³. Step 4: At 2 cm³/s, time=100 s=20z, hence z=5.