Student Login

Home›Chapters›Work, Energy and Power PYQs›Spring & Elastic Energy›Question 27

JEE Main 2007 (AIEEE) · Spring & Elastic Energy

Spring & Elastic Energy question from JEE Main 2007 (AIEEE)

Q27JEE Main 2007 · AIEEEMedium

Spring & Elastic Energy

A $2\text{ kg}$ block slides on a horizontal floor with a speed of $4\text{ m/s}.$ It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is $15\text{ N}$ and spring constant is $10{,}000\text{ N/m}.$ The spring compresses by

Show answer and solution

Answer: (b)

Work-energy: $\frac{1}{2}mv^2 = fx + \frac{1}{2}kx^2$ .
$16 = 15x + 5000x^2 \Rightarrow 5000x^2 + 15x - 16 = 0$
$x = \frac{-15 + \sqrt{225 + 320000}}{10000} \approx 0.055$ m
So the answer is (b) $5.5$ cm.

Report a mistake

More questions on Spring & Elastic Energy

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height…NEET 2007 (AIPMT)
The potential energy of a long spring when stretched by 2 cm is U. If the spring is…NEET 2006 (AIPMT)
A mass of 0.5 kg moving with a speed of 1.5 m/s on horizontal smooth surface, collides…NEET 2004 (AIPMT)
When a long spring is stretched by 2 cm, its potential energy is U. If the spring is…NEET 2003 (AIPMT)
A spring of spring constant 5 × 10³ N/m is stretched initially by 5 cm from the…JEE Main 2003 (AIEEE)
A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending…JEE Main 2002 (AIEEE)
Two springs A and B having spring constant KA and KB (KA = 2KB) are stretched by applying…NEET 2001 (AIPMT)
A block of mass 'm' moving on a frictionless horizontal surface collides with a spring of…MHT CET 2026 (16 Apr, Shift 1)