An ideal spring, with a pointer attached to its end, hangs next to a scale. With a 100 N weight attached and at rest, the pointer indicates '40' cm on the scale as shown. Using a 200 N weigh

Question

An ideal spring, with a pointer attached to its end, hangs next to a scale. With a 100 N weight attached and at rest, the pointer indicates '40' cm on the scale as shown. Using a 200 N weight instead results in 60 cm on the scale. Using an unknown weight 'X' instead results in '30' cm on the scale. Fill value of 10 X ​ (in newton).

TestHub · Accepted Answer

100 = k × ( 40 − ℓ 0 ​ ) ​ 200 = k × ( 60 − ℓ 0 ​ ) ​ 2 = 40 − ℓ 0 ​ 60 − ℓ 0 ​ ​ ​ 80 − 2 ℓ 0 ​ = 60 − ℓ 0 ​ ​ 20 = ℓ 0 ​ ⇒ 20 k = 100 ⇒ k = 5 ​ x = k × ( 30 − 20 ) = 50 N ​

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