A brass bar of cross-section 10 cm² has consecutive lengths AB=60 cm, BC=100 cm, CD=120 cm. Axial forces 5 t left at A, 3 t right at B, 1 t right at C, 1 t right at D act as shown. Y=8×10² t/cm². Total extension is (30+x)×5ʸ×10⁻⁴ cm; find xy.
Physics · Mixed Chapter
JEE Main Practice

Question

A brass bar of cross-section 10 cm² has consecutive lengths AB=60 cm, BC=100 cm, CD=120 cm. Axial forces 5 t left at A, 3 t right at B, 1 t right at C, 1 t right at D act as shown. Y=8×10² t/cm². Total extension is (30+x)×5ʸ×10⁻⁴ cm; find xy.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Axial forces in AB, BC and CD are 5 t, (5−3)=2 t and (5−3−1)=1 t. Step 2: Each segment extension is FL/(YA). Total ΔL=[5×60+2×100+1×120]/(8×10²×10) cm. Step 3: ΔL=620/8000=0.0775 cm=775×10⁻⁴ cm. Step 4: 775=31×25=(30+1)×5². Therefore x=1, y=2 and xy=2.