The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, potential energy stored in it will be:

1. | \(16U\) | 2. | \(2U\) |

3. | \(4U\) | 4. | \(8U\) |

Subtopic: Elastic Potential Energy |

71%

From NCERT

NEET - 2023

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A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:

(The friction between the block and the surface is negligible).

1. | \(u\sqrt{\frac{m}{k}}\) | 2. | \(4u\sqrt{\frac{m}{k}}\) |

3. | \(2u\sqrt{\frac{m}{k}}\) | 4. | \(\frac12u\sqrt{\frac{k}{m}}\) |

Subtopic: Elastic Potential Energy |

79%

From NCERT

NEET - 2022

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Two similar springs \(P\) and \(Q\) have spring constants \(k_P\) and \(k_Q\), such that \(k_P>k_Q\). They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs \(W_P\)_{ }and \(W_Q\) are related as, in case (a) and case (b), respectively:

1. | \(W_P=W_Q;~W_P>W_Q\) |

2. | \(W_P=W_Q;~W_P=W_Q\) |

3. | \(W_P>W_Q;~W_P<W_Q\) |

4. | \(W_P<W_Q;~W_P<W_Q\) |

Subtopic: Elastic Potential Energy |

73%

From NCERT

NEET - 2015

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A block of mass \(M\) is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant value of \(k\). The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

1. \(Mg/k\)

2. \(2Mg/k\)

3. \(4Mg/k\)

4. \(Mg/2k\)

1. \(Mg/k\)

2. \(2Mg/k\)

3. \(4Mg/k\)

4. \(Mg/2k\)

Subtopic: Elastic Potential Energy |

69%

From NCERT

AIPMT - 2009

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A vertical spring with a force constant *\(k\)* is fixed on a table. A ball of mass *\(m\)* at a height *\(h\)* above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance *\(d\)*. The net work done in the process is:

1. \(mg(h+d)+\frac{1}{2}kd^2\)

2. \(mg(h+d)-\frac{1}{2}kd^2\)

3. \(mg(h-d)-\frac{1}{2}kd^2\)

4. \(mg(h-d)+\frac{1}{2}kd^2\)

Subtopic: Elastic Potential Energy |

64%

From NCERT

AIPMT - 2007

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The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:

1. \(4U\)

2. \(8U\)

3. \(16U\)

4. \(U/4\)

Subtopic: Elastic Potential Energy |

78%

From NCERT

AIPMT - 2006

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A mass of \(0.5\) kg moving with a speed of \(1.5\) m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50\) N/m. The maximum compression of the spring would be:

1. \(0.12\) m

2. \(1.5\) m

3. \(0.5\) m

4. \(0.15\) m

Subtopic: Elastic Potential Energy |

80%

From NCERT

AIPMT - 2004

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When a long spring is stretched by \(2\) cm, its potential energy is \(U\). If the spring is stretched by \(10\) cm, the potential energy stored in it will be:

1. \(U/5\)

2. \(5U\)

3. \(10U\)

4. \(25U\)

Subtopic: Elastic Potential Energy |

87%

From NCERT

AIPMT - 2003

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Two springs A and B having spring constant ${K}_{A}$ $and$ ${K}_{B}$ $$ $({K}_{A}$ $=$ $2{K}_{B})$ are stretched by applying a force of equal magnitude. If the energy stored in spring A is E, then the energy stored in B will be:

1. 2E

2. $\frac{E}{4}$

3. $\frac{E}{2}$

4. 4E

Subtopic: Elastic Potential Energy |

68%

From NCERT

AIPMT - 2001

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If two springs, A and B $({K}_{A}$ $=$ $2$ ${K}_{B}),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:

1. 1 : 2

2. 2 : 1

3. 1 : 1

4. 1 : 4

Subtopic: Elastic Potential Energy |

62%

From NCERT

AIPMT - 1999

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