A circular disc reaches from top to bottom of an inclined plane of length $$l$$. When it slips down the plane, if takes $$t \mathrm{~s}$$. When it rolls down the plane then it takes $$\left(\frac{\alpha}{2}\right)^{1 / 2} t \mathrm{~s}$$, where $$\alpha$$ is _________.

A force $$(3 x^2+2 x-5) \mathrm{N}$$ displaces a body from $$x=2 \mathrm{~m}$$ to $$x=4 \mathrm{~m}$$. Work done by this force is ________ J.

A particle of mass $$0.50 \mathrm{~kg}$$ executes simple harmonic motion under force $$F=-50(\mathrm{Nm}^{-1}) x$$. The time period of oscillation is $$\frac{x}{35} s$$. The value of $$x$$ is _________.

(Given $$\pi=\frac{22}{7}$$)

At room temperature $$(27^{\circ} \mathrm{C})$$, the resistance of a heating element is $$50 \Omega$$. The temperature coefficient of the material is $$2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$$. The temperature of the element, when its resistance is $$62 \Omega$$, is __________$${ }^{\circ} \mathrm{C}$$.