A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is 

(1) $Mg\frac{d}{4}$

(2) $3Mg\frac{d}{4}$

(3) $-3Mg\frac{d}{4}$

(4) Mgd 

Two springs have their force constant as k₁ and $k_2(k_1>k_2)$. When they are stretched by the same force 

(1) No work is done in case of both the springs

(2) Equal work is done in case of both the springs

(3) More work is done in case of second spring

(4) More work is done in case of first spring

The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be:

(1) 30

(2) 40

(3) 10

(4) 20

A spring of force constant 800 N/m has an extension of 5cm. The work done in extending it from 5cm to 15 cm is:

(1) 16 J

(2) 8 J

(3) 32 J

(4) 24 J

A spring of spring constant 5 × 10³ N/m is stretched initially by 5cm from the unstretched position. Then the work required to stretch it further by another 5 cm is 

(1) 6.25 N-m

(2) 12.50 N-m

(3) 18.75 N-m

(4) 25.00 N-m

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

(1) 0.15 m

(2) 0.12 m

(3) 1.5 m

(4) 0.5 m

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to- 

(1) x²

(2) e^x

(3) x

(4) log_e x

The spring extends by x on loading, then energy stored by the spring is : (if T is the tension in spring and k is spring constant) 

(1) $\frac{T^2}{2k}$

(2) $\frac{T^2}{2k^2}$

(3) $\frac{2k}{T^2}$

(4) $\frac{2T^2}{k}$

The potential energy of a body is given by, U = A – Bx² (Where x is the displacement). The magnitude of force acting on the particle is 

(1) Constant

(2) Proportional to x

(3) Proportional to x²

(4) Inversely proportional to x

The potential energy between two atoms in a molecule is given by $$\(U\left ( x \right )=\frac{a}{x^{12}}-\frac{b}{x^{6}};\) where \(a\) and \(b\) are positive constants and \(x\) is the distance between the atoms. The atoms are in stable equilibrium when:
1. \(x=\sqrt[6]{\frac{11a}{5b}}\)
2. \(x=\sqrt[6]{\frac{a}{2b}}\)
3. \(x=0\)
4. \(x=\sqrt[6]{\frac{2a}{b}}\)