Question

It has recently become possible to "weigh" DNA molecules by measuring the influence of their mass on a nano-oscillator. Figure shows a thin rectangular cantilever etched out of silicon (density 2300 kg/m3) with a small gold dot at the end. If pulled down and released, the end of the cantilever vibrates with simple harmonic motion, moving up and down like a diving board after a jump. When bathed with DNA molecules whose ends have been modified to bind with gold, one or more molecules may attach to the gold dot. The addition of their mass causes a very slight-but measurable-decrease in the oscillation frequency. A vibrating cantilever of mass M can be modeled as a block of mass 13M attached to a spring. (The factor of 13 arises from the moment of inertia of a bar pivoted at one end.) Neither the mass nor the spring constant can be determined very accurately-perhaps to only two significant figures-but the oscillation frequency can be measured with very high precision simply by counting the oscillations. In one experiment, the cantilever was initially vibrating at exactly 14 MHz . Attachment of a DNA molecule caused the frequency to decrease by 56 Hz .

4000 nm ↓ 400 nm Thickness = 100 nm

What was the mass of the DNA?

Express your answer to two significant figures and include the appropriate units.

Answer 1

mass=volume×density=length×breadth×thickness×density

(cantilever is in the form of rectangle).

Frequency of oscillation of loaded spring depends on mass so as mass increases frequency ofooscillation decreases.